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arXiv · 1805.01714

Intersection numbers of twisted cycles and cocycles for degenerate arrangements

Yoshiaki Goto
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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.

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Yoshiaki Goto. 2018-05-04. Intersection numbers of twisted cycles and cocycles for degenerate arrangements. https://arxiv.org/abs/1805.01714

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