Intersection numbers of twisted cycles and cocycles for degenerate arrangements

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.

Holonomic Gradient Method for Two Way Contingency Tables

“…In general, contiguity relations and Pfaffian systems for such hypergeometric functions become complicated. In [9], a method is put forward to evaluate intersection numbers and contiguity relations when only one p ij is zero.…”