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LENGTH AND DECOMPOSITION OF THE COHOMOLOGY OF THE COMPLEMENT TO A HYPERPLANE ARRANGEMENT
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22019 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 147, no 5, p. 2265-2273Article in journal (Refereed) Published
Abstract [en]

Let A be a hyperplane arrangement in C-n. We prove in an elementary way that the number of decomposition factors as a perverse sheaf of the direct image Rj(*) C-(U) over tilde[n] of the constant sheaf on the complement (U) over tilde to the arrangement is given by the Poincare polynomial of the arrangement. Furthermore, we describe the decomposition factors of Rj(*) C-(U) over tilde[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].

Place, publisher, year, edition, pages
2019. Vol. 147, no 5, p. 2265-2273
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-168318DOI: 10.1090/proc/14379ISI: 000464314900038OAI: oai:DiVA.org:su-168318DiVA, id: diva2:1315708
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-14Bibliographically approved

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