Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers
Abstract In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Ca...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Choi, Youngook [verfasserIn] Iliev, Hristo [verfasserIn] Kim, Seonja [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: Mediterranean journal of mathematics - Springer International Publishing, 2004, 21(2024), 4 vom: Juni |
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| Übergeordnetes Werk: |
volume:21 ; year:2024 ; number:4 ; month:06 |
| Links: |
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| DOI / URN: |
10.1007/s00009-024-02668-3 |
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| Katalog-ID: |
SPR05609339X |
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| 520 | |a Abstract In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. | ||
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| 650 | 4 | |a ruled surfaces |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a triple coverings |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a curves on cones |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Iliev, Hristo |e verfasserin |4 aut | |
| 700 | 1 | |a Kim, Seonja |e verfasserin |4 aut | |
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10.1007/s00009-024-02668-3 doi (DE-627)SPR05609339X (SPR)s00009-024-02668-3-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Choi, Youngook verfasserin aut Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. Hilbert scheme of curves (dpeaa)DE-He213 ruled surfaces (dpeaa)DE-He213 triple coverings (dpeaa)DE-He213 curves on cones (dpeaa)DE-He213 Iliev, Hristo verfasserin aut Kim, Seonja verfasserin aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 21(2024), 4 vom: Juni (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:21 year:2024 number:4 month:06 https://dx.doi.org/10.1007/s00009-024-02668-3 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_267 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_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 31.00 VZ AR 21 2024 4 06 |
| spelling |
10.1007/s00009-024-02668-3 doi (DE-627)SPR05609339X (SPR)s00009-024-02668-3-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Choi, Youngook verfasserin aut Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. Hilbert scheme of curves (dpeaa)DE-He213 ruled surfaces (dpeaa)DE-He213 triple coverings (dpeaa)DE-He213 curves on cones (dpeaa)DE-He213 Iliev, Hristo verfasserin aut Kim, Seonja verfasserin aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 21(2024), 4 vom: Juni (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:21 year:2024 number:4 month:06 https://dx.doi.org/10.1007/s00009-024-02668-3 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_267 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_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 31.00 VZ AR 21 2024 4 06 |
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10.1007/s00009-024-02668-3 doi (DE-627)SPR05609339X (SPR)s00009-024-02668-3-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Choi, Youngook verfasserin aut Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. Hilbert scheme of curves (dpeaa)DE-He213 ruled surfaces (dpeaa)DE-He213 triple coverings (dpeaa)DE-He213 curves on cones (dpeaa)DE-He213 Iliev, Hristo verfasserin aut Kim, Seonja verfasserin aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 21(2024), 4 vom: Juni (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:21 year:2024 number:4 month:06 https://dx.doi.org/10.1007/s00009-024-02668-3 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_267 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_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 31.00 VZ AR 21 2024 4 06 |
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10.1007/s00009-024-02668-3 doi (DE-627)SPR05609339X (SPR)s00009-024-02668-3-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Choi, Youngook verfasserin aut Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. Hilbert scheme of curves (dpeaa)DE-He213 ruled surfaces (dpeaa)DE-He213 triple coverings (dpeaa)DE-He213 curves on cones (dpeaa)DE-He213 Iliev, Hristo verfasserin aut Kim, Seonja verfasserin aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 21(2024), 4 vom: Juni (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:21 year:2024 number:4 month:06 https://dx.doi.org/10.1007/s00009-024-02668-3 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_267 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_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 31.00 VZ AR 21 2024 4 06 |
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10.1007/s00009-024-02668-3 doi (DE-627)SPR05609339X (SPR)s00009-024-02668-3-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Choi, Youngook verfasserin aut Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. Hilbert scheme of curves (dpeaa)DE-He213 ruled surfaces (dpeaa)DE-He213 triple coverings (dpeaa)DE-He213 curves on cones (dpeaa)DE-He213 Iliev, Hristo verfasserin aut Kim, Seonja verfasserin aut Enthalten in Mediterranean journal of mathematics Springer International Publishing, 2004 21(2024), 4 vom: Juni (DE-627)394566831 (DE-600)2160803-9 1660-5454 nnns volume:21 year:2024 number:4 month:06 https://dx.doi.org/10.1007/s00009-024-02668-3 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_267 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_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 31.00 VZ AR 21 2024 4 06 |
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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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. 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| author |
Choi, Youngook |
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Choi, Youngook ddc 510 bkl 31.00 misc Hilbert scheme of curves misc ruled surfaces misc triple coverings misc curves on cones Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers |
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510 VZ 31.00 bkl Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers Hilbert scheme of curves (dpeaa)DE-He213 ruled surfaces (dpeaa)DE-He213 triple coverings (dpeaa)DE-He213 curves on cones (dpeaa)DE-He213 |
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ddc 510 bkl 31.00 misc Hilbert scheme of curves misc ruled surfaces misc triple coverings misc curves on cones |
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Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers |
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non-reduced components of the hilbert scheme of curves using triple covers |
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Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers |
| abstract |
Abstract In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. © 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. © 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 In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $$\gamma $$ and degree e in $${\mathbb {P}}^{e-\gamma }$$. Using the free resolution of the ideal of such a curve found by Catalisano and Gimigliano, and a technique concerning deformations of curves introduced by Ciliberto, we show that the deformations of such curves remain on cones over a deformation of the base curve. This allows us to prove that for $$\gamma \ge 3$$ and $$e \ge 4\gamma + 5$$, there exists a non-reduced component $${\mathcal {H}}$$ of the Hilbert scheme of smooth curves of genus $$3e + 3\gamma $$ and degree $$3e+1$$ in $${\mathbb {P}}^{e-\gamma +1}$$. We show that $$\dim T_{[X]} {\mathcal {H}} = \dim {\mathcal {H}} + 1 = (e - \gamma + 1)^2 + 7e + 5$$ for a general point $$[X] \in {\mathcal {H}}$$. © 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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4 |
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Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers |
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https://dx.doi.org/10.1007/s00009-024-02668-3 |
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Iliev, Hristo Kim, Seonja |
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10.1007/s00009-024-02668-3 |
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2024-07-03T20:10:09.543Z |
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|
| score |
7.400614 |