Intersection numbers of twisted cycles and cocycles for degenerate arrangements

2018/05/04 by Goto, Yoshiaki
#32S22 #33C70 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.01714

Abstract

We study the intersection numbers defined on twisted homology or cohomology groups that are associated with hypergeometric integrals corresponding to degenerate hyperplane arrangements in the projective k-space. We present formulas to evaluate the intersection numbers in the case when exactly one (k+1)-tuple of the hyperplanes intersects at a point. As an application, we discuss the contiguity relations of hypergeometric functions in terms of the intersection numbers on twisted cohomology groups.

Related

• Intersection numbers of twisted homology and cohomology groups associated to the Riemann-Wirtinger integral
• Intersection numbers and twisted period relations for the generalized hypergeometric function _m+1 F_m
• An algorithm of computing cohomology intersection number of hypergeometric integrals
• Intersection Numbers in Quantum Mechanics and Field Theory
• Computing cohomology intersection numbers of GKZ hypergeometric systems