On the geometry of toric arrangements

2005/05/17 by Corrado De Concini, C. De Concini, Claudio Procesi +3 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.math/0505351

arxiv created 2005/06/08 · arxiv updated 2009/12/01

Abstract

We introduce toric arrangements, essentially finite families of codimension 1 subtori of a torus or of their cosets, as a periodic generalization of hyperplane arrangements, compute cohomology of the complement of such an arrangement and apply the theory to give a geometric interpretation of the formulas of Brion--Szenes--Vergne counting the number of integral points in polytopes.

Cited by

• Elliptic arrangements of complex multiplication type
• Partial fraction decompositions and an algorithm for computing the vector partition function

Related

• The homotopy type of toric arrangements
• Torus actions and combinatorics of polytopes
• The integer cohomology algebra of toric arrangements
• The Goresky-MacPherson formula for toric arrangements
• Complements of hyperplane arrangements as posets of spaces