On a generalization of Solomon-Terao formula for subspace arrangements

We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Pol, Delphine [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues

Übergeordnetes Werk:	Enthalten in: Journal of algebra - San Diego, Calif. : Elsevier, 1964, 560, Seite 266-295
Übergeordnetes Werk:	volume:560 ; pages:266-295

DOI / URN:	10.1016/j.jalgebra.2020.05.011

Katalog-ID:	ELV004454928

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245	1	0	\|a On a generalization of Solomon-Terao formula for subspace arrangements
264		1	\|c 2020
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520			\|a We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension.
650		4	\|a Subspace arrangements
650		4	\|a Solomon-Terao formula
650		4	\|a Hilbert-Poincaré series
650		4	\|a Logarithmic differential forms
650		4	\|a Logarithmic residues
773	0	8	\|i Enthalten in \|t Journal of algebra \|d San Diego, Calif. : Elsevier, 1964 \|g 560, Seite 266-295 \|h Online-Ressource \|w (DE-627)266890423 \|w (DE-600)1468947-9 \|w (DE-576)10337311X \|x 1090-266X \|7 nnns
773	1	8	\|g volume:560 \|g pages:266-295
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936	b	k	\|a 31.20 \|j Algebra: Allgemeines
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matchkey_str	article:1090266X:2020----::ngnrlztooslmneafruaosb
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publishDate	2020
allfields	10.1016/j.jalgebra.2020.05.011 doi (DE-627)ELV004454928 (ELSEVIER)S0021-8693(20)30262-3 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Pol, Delphine verfasserin aut On a generalization of Solomon-Terao formula for subspace arrangements 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension. Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 560, Seite 266-295 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:560 pages:266-295 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 560 266-295
spelling	10.1016/j.jalgebra.2020.05.011 doi (DE-627)ELV004454928 (ELSEVIER)S0021-8693(20)30262-3 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Pol, Delphine verfasserin aut On a generalization of Solomon-Terao formula for subspace arrangements 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension. Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 560, Seite 266-295 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:560 pages:266-295 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 560 266-295
allfields_unstemmed	10.1016/j.jalgebra.2020.05.011 doi (DE-627)ELV004454928 (ELSEVIER)S0021-8693(20)30262-3 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Pol, Delphine verfasserin aut On a generalization of Solomon-Terao formula for subspace arrangements 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension. Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 560, Seite 266-295 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:560 pages:266-295 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 560 266-295
allfieldsGer	10.1016/j.jalgebra.2020.05.011 doi (DE-627)ELV004454928 (ELSEVIER)S0021-8693(20)30262-3 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Pol, Delphine verfasserin aut On a generalization of Solomon-Terao formula for subspace arrangements 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension. Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 560, Seite 266-295 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:560 pages:266-295 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 560 266-295
allfieldsSound	10.1016/j.jalgebra.2020.05.011 doi (DE-627)ELV004454928 (ELSEVIER)S0021-8693(20)30262-3 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Pol, Delphine verfasserin aut On a generalization of Solomon-Terao formula for subspace arrangements 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension. Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 560, Seite 266-295 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:560 pages:266-295 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 560 266-295
language	English
source	Enthalten in Journal of algebra 560, Seite 266-295 volume:560 pages:266-295
sourceStr	Enthalten in Journal of algebra 560, Seite 266-295 volume:560 pages:266-295
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bklname	Algebra: Allgemeines
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topic_facet	Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues
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author	Pol, Delphine
spellingShingle	Pol, Delphine ddc 510 bkl 31.20 misc Subspace arrangements misc Solomon-Terao formula misc Hilbert-Poincaré series misc Logarithmic differential forms misc Logarithmic residues On a generalization of Solomon-Terao formula for subspace arrangements
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topic_title	510 DE-600 31.20 bkl On a generalization of Solomon-Terao formula for subspace arrangements Subspace arrangements Solomon-Terao formula Hilbert-Poincaré series Logarithmic differential forms Logarithmic residues
topic	ddc 510 bkl 31.20 misc Subspace arrangements misc Solomon-Terao formula misc Hilbert-Poincaré series misc Logarithmic differential forms misc Logarithmic residues
topic_unstemmed	ddc 510 bkl 31.20 misc Subspace arrangements misc Solomon-Terao formula misc Hilbert-Poincaré series misc Logarithmic differential forms misc Logarithmic residues
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title	On a generalization of Solomon-Terao formula for subspace arrangements
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title_full	On a generalization of Solomon-Terao formula for subspace arrangements
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title_sort	on a generalization of solomon-terao formula for subspace arrangements
title_auth	On a generalization of Solomon-Terao formula for subspace arrangements
abstract	We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension.
abstractGer	We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension.
abstract_unstemmed	We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension.
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title_short	On a generalization of Solomon-Terao formula for subspace arrangements
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV004454928</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230524131329.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230502s2020 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jalgebra.2020.05.011</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV004454928</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0021-8693(20)30262-3</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.20</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pol, Delphine</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On a generalization of Solomon-Terao formula for subspace arrangements</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. 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On a generalization of Solomon-Terao formula for subspace arrangements

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