Cohomology of abelian arrangements

Abstract

An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. In this paper, we study the cohomology of the complement of an abelian arrangement. For unimodular abelian arrangements, we provide a combinatorial presentation for a differential graded algebra whose cohomology is isomorphic to the rational cohomology of the complement. Moreover, this DGA has a bi-grading that allows us to compute the mixed Hodge numbers.

11 pages; to appear in Proceedings of the American Mathematical Society

References in corpus (1)

• Around the tangent cone theorem

Cited by in corpus (24)

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• Around the tangent cone theorem
• Combinatorial covers and vanishing of cohomology
• Representation stability for the cohomology of arrangements associated to root systems
• Abelian duality and propagation of resonance
• Two Examples of Toric Arrangements
• Quadratic-linear duality and rational homotopy theory of chordal arrangements
• A Leray model for the Orlik-Solomon algebra
• On the cohomology of arrangements of subtori
• Combinatorics of orbit configuration spaces
• Set of independencies and Tutte polynomial of matroids over a domain
• Poincaré polynomial of elliptic arrangements is not a specialization of the Tutte polynomial
• Stanley-Reisner rings for symmetric simplicial complexes, G-semimatroids and Abelian arrangements
• Deletion-restriction in toric arrangements
• Cohomology ring of manifold arrangements
• The homotopy type of elliptic arrangements
• Length of Perverse Sheaves on Hyperplane Arrangements
• The cohomology rings of the unordered configuration spaces of the torus
• Configuration space in a product
• The localization spectral sequence in the motivic setting
• Cohomology of configuration spaces on punctured varieties
• Cohomology ring of non-compact abelian arrangements