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LENGTH AND DECOMPOSITION OF THE COHOMOLOGY OF THE COMPLEMENT TO A HYPERPLANE ARRANGEMENT.
- Source :
- Proceedings of the American Mathematical Society; May2019, Vol. 147 Issue 5, p2265-2273, 9p
- Publication Year :
- 2019
-
Abstract
- Let A be a hyperplane arrangement in C<superscript>n</superscript>. We prove in an elementary way that the number of decomposition factors as a perverse sheaf of the direct image Rj*C<subscript>Ũ</subscript> [n] of the constant sheaf on the complement Ũ to the arrangement is given by the Poincar'e polynomial of the arrangement. Furthermore, we describe the decomposition factors of Rj*C<subscript>Ũ</subscript> [n] as certain local cohomology sheaves and give their multiplicity. These results are implicitly contained, with different proofs, in Looijenga [Contemp. Math., 150 (1993), pp. 205-228], Budur and Saito [Math. Ann., 347 (2010), no. 3, 545-579], Petersen [Geom. Topol., 21 (2017), no. 4, 2527-2555], and Oaku [Length and multiplicity of the local cohomology with support in a hyperplane arrangement, arXiv:1509.01813v1]. [ABSTRACT FROM AUTHOR]
- Subjects :
- MULTIPLICITY (Mathematics)
MATHEMATICS
SHEAF theory
POLYNOMIALS
EVIDENCE
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 147
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 135859397
- Full Text :
- https://doi.org/10.1090/proc/14379