Length and decomposition of the cohomology of the complement to a\n hyperplane arrangement

2017/03/22 by Rikard Bøgvad, Bøgvad, Rikard, Iara Gonçalves +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1703.07662

openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let mathcal A be a hyperplane arrangement in mathbb Cⁿ. We show that\nthe number of decomposition factors as a perverse sheaf of the direct image\nRj_* mathbb C_U of the constant sheaf on the complement U to the\narrangement is given by the Poincar 'e polynomial of the arrangement.\nFurthermore we describe the composition factors of Rj_* mathbb C_U as\ncertain local cohomology sheaves and give their multiplicity.\n

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