Higher rank flag sheaves on surfaces
Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability con...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sheshmani, Artan [verfasserIn] Yau, Shing-Tung [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: European journal of mathematics - Springer International Publishing, 2015, 10(2024), 3 vom: 16. Juli |
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| Übergeordnetes Werk: |
volume:10 ; year:2024 ; number:3 ; day:16 ; month:07 |
| Links: |
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| DOI / URN: |
10.1007/s40879-024-00752-2 |
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| Katalog-ID: |
SPR056617984 |
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| 520 | |a Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . | ||
| 650 | 4 | |a Donaldson–Thomas invariants |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Flag sheaves |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stability conditions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Deformation-obstruction theory |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Vafa–Witten invariants |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Yau, Shing-Tung |e verfasserin |4 aut | |
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10.1007/s40879-024-00752-2 doi (DE-627)SPR056617984 (SPR)s40879-024-00752-2-e DE-627 ger DE-627 rakwb eng 510 VZ Sheshmani, Artan verfasserin aut Higher rank flag sheaves on surfaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . Donaldson–Thomas invariants (dpeaa)DE-He213 Flag sheaves (dpeaa)DE-He213 Stability conditions (dpeaa)DE-He213 Deformation-obstruction theory (dpeaa)DE-He213 Vafa–Witten invariants (dpeaa)DE-He213 Yau, Shing-Tung verfasserin aut Enthalten in European journal of mathematics Springer International Publishing, 2015 10(2024), 3 vom: 16. Juli (DE-627)815914067 (DE-600)2806605-4 2199-6768 nnns volume:10 year:2024 number:3 day:16 month:07 https://dx.doi.org/10.1007/s40879-024-00752-2 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 3 16 07 |
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10.1007/s40879-024-00752-2 doi (DE-627)SPR056617984 (SPR)s40879-024-00752-2-e DE-627 ger DE-627 rakwb eng 510 VZ Sheshmani, Artan verfasserin aut Higher rank flag sheaves on surfaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . Donaldson–Thomas invariants (dpeaa)DE-He213 Flag sheaves (dpeaa)DE-He213 Stability conditions (dpeaa)DE-He213 Deformation-obstruction theory (dpeaa)DE-He213 Vafa–Witten invariants (dpeaa)DE-He213 Yau, Shing-Tung verfasserin aut Enthalten in European journal of mathematics Springer International Publishing, 2015 10(2024), 3 vom: 16. Juli (DE-627)815914067 (DE-600)2806605-4 2199-6768 nnns volume:10 year:2024 number:3 day:16 month:07 https://dx.doi.org/10.1007/s40879-024-00752-2 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 3 16 07 |
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10.1007/s40879-024-00752-2 doi (DE-627)SPR056617984 (SPR)s40879-024-00752-2-e DE-627 ger DE-627 rakwb eng 510 VZ Sheshmani, Artan verfasserin aut Higher rank flag sheaves on surfaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . Donaldson–Thomas invariants (dpeaa)DE-He213 Flag sheaves (dpeaa)DE-He213 Stability conditions (dpeaa)DE-He213 Deformation-obstruction theory (dpeaa)DE-He213 Vafa–Witten invariants (dpeaa)DE-He213 Yau, Shing-Tung verfasserin aut Enthalten in European journal of mathematics Springer International Publishing, 2015 10(2024), 3 vom: 16. Juli (DE-627)815914067 (DE-600)2806605-4 2199-6768 nnns volume:10 year:2024 number:3 day:16 month:07 https://dx.doi.org/10.1007/s40879-024-00752-2 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 3 16 07 |
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10.1007/s40879-024-00752-2 doi (DE-627)SPR056617984 (SPR)s40879-024-00752-2-e DE-627 ger DE-627 rakwb eng 510 VZ Sheshmani, Artan verfasserin aut Higher rank flag sheaves on surfaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . Donaldson–Thomas invariants (dpeaa)DE-He213 Flag sheaves (dpeaa)DE-He213 Stability conditions (dpeaa)DE-He213 Deformation-obstruction theory (dpeaa)DE-He213 Vafa–Witten invariants (dpeaa)DE-He213 Yau, Shing-Tung verfasserin aut Enthalten in European journal of mathematics Springer International Publishing, 2015 10(2024), 3 vom: 16. Juli (DE-627)815914067 (DE-600)2806605-4 2199-6768 nnns volume:10 year:2024 number:3 day:16 month:07 https://dx.doi.org/10.1007/s40879-024-00752-2 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 3 16 07 |
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10.1007/s40879-024-00752-2 doi (DE-627)SPR056617984 (SPR)s40879-024-00752-2-e DE-627 ger DE-627 rakwb eng 510 VZ Sheshmani, Artan verfasserin aut Higher rank flag sheaves on surfaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . Donaldson–Thomas invariants (dpeaa)DE-He213 Flag sheaves (dpeaa)DE-He213 Stability conditions (dpeaa)DE-He213 Deformation-obstruction theory (dpeaa)DE-He213 Vafa–Witten invariants (dpeaa)DE-He213 Yau, Shing-Tung verfasserin aut Enthalten in European journal of mathematics Springer International Publishing, 2015 10(2024), 3 vom: 16. Juli (DE-627)815914067 (DE-600)2806605-4 2199-6768 nnns volume:10 year:2024 number:3 day:16 month:07 https://dx.doi.org/10.1007/s40879-024-00752-2 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 3 16 07 |
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Enthalten in European journal of mathematics 10(2024), 3 vom: 16. Juli volume:10 year:2024 number:3 day:16 month:07 |
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Donaldson–Thomas invariants Flag sheaves Stability conditions Deformation-obstruction theory Vafa–Witten invariants |
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Sheshmani, Artan @@aut@@ Yau, Shing-Tung @@aut@@ |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, .</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Donaldson–Thomas invariants</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Flag sheaves</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability conditions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation-obstruction theory</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Vafa–Witten invariants</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yau, Shing-Tung</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">European journal of mathematics</subfield><subfield code="d">Springer International Publishing, 2015</subfield><subfield code="g">10(2024), 3 vom: 16. 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Sheshmani, Artan |
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Sheshmani, Artan ddc 510 misc Donaldson–Thomas invariants misc Flag sheaves misc Stability conditions misc Deformation-obstruction theory misc Vafa–Witten invariants Higher rank flag sheaves on surfaces |
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510 VZ Higher rank flag sheaves on surfaces Donaldson–Thomas invariants (dpeaa)DE-He213 Flag sheaves (dpeaa)DE-He213 Stability conditions (dpeaa)DE-He213 Deformation-obstruction theory (dpeaa)DE-He213 Vafa–Witten invariants (dpeaa)DE-He213 |
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Higher rank flag sheaves on surfaces |
| abstract |
Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract We study moduli space of holomorphic triples $$E_{1}\xrightarrow {\scriptscriptstyle \phi } E_{2}$$, composed of torsion-free sheaves $$E_{i}$$, $$i=1,2$$, and a holomorphic mophism between them, over a smooth complex projective surface S. The triples are equipped with Schmitt stability condition (Schmitt in Algebras Represent Theory 6(1):1–32, 2000). We observe that when Schmitt stability parameter q(m) becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute deformation-obstruction theory in some cases. We further generalize our construction by gluing triple moduli spaces, and extend the earlier work (Gholampour et al. in Nested Hilbert schemes on surfaces: virtual fundamental class, preprint, arXiv:1701.08899) where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of chains E1→ϕ1E2→ϕ2⋯→ϕn-1En,$$\begin{aligned} E_{1}\xrightarrow { \ \phi _{1} \ } E_{2}\xrightarrow { \ \phi _{2} \ } \cdots \xrightarrow { \ \phi _{n-1} \ } E_{n}, \end{aligned}$$where $$\phi _{i}$$ are injective morphisms and $$\textrm{rk}\hspace{0.55542pt}(E_{i})\geqslant 1$$ for all i. There is a connection, by wallcrossing in the master space, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of threefold given by a line bundle on the surface, . © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| title_short |
Higher rank flag sheaves on surfaces |
| url |
https://dx.doi.org/10.1007/s40879-024-00752-2 |
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| author2 |
Yau, Shing-Tung |
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Yau, Shing-Tung |
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10.1007/s40879-024-00752-2 |
| up_date |
2024-10-08T05:15:04.308Z |
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| score |
7.165477 |