Homology and cohomology intersection numbers of GKZ systems

2020/06/14 by Goto, Yoshiaki, Matsubara-Heo, Saiei-Jaeyeong
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.07848

Abstract

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology intersection numbers in terms of a Laurent series. We show that the cohomology intersection number depends rationally on the parameters. We also prove a conjecture of F. Beukers and C. Verschoor on the signature of the monodromy invariant hermitian form. This is a continuation of the previous work arXiv:1904.00565.

Related

• Computing cohomology intersection numbers of GKZ hypergeometric systems
• On the Holonomic Rank Problem
• Remarks on the combinatorial intersection cohomology of fans
• Intersection numbers and twisted period relations for the generalized hypergeometric function _m+1 F_m
• Intersection numbers of twisted cycles and cocycles for degenerate arrangements