Cohomology of Complements of Toric Arrangements Associated to Root Systems

2016/01/08 by Bergvall, Olof
#05E18 #14F40 (Primary) #14N20 #52C35 (Secondary) #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.01857

Abstract

We compute the cohomology of the complement of toric arrangements associated to root systems as representations of the corresponding Weyl groups. Specifically, we develop an algorithm for computing the cohomology of the complement of toric arrangements associated to general root systems and we carry out this computation for the exceptional root systems G₂, F₄, E₆ and E₇. We also compute the total cohomology of the complement of the toric arrangement associated to A_n as a representation of the Weyl group and give a formula for its Poincaré polynomial.

Related

• A basis for the cohomology of compact models of toric arrangements
• Combinatorial generators for the cohomology of toric arrangements
• The integer cohomology of toric Weyl arrangements
• The cohomology groups of real toric varieties associated to Weyl chambers of type C and D
• The homotopy type of toric arrangements