Appell-Lauricella's hypergeometric functions and intersection theory

Abstract

We study hypergeometric functions by applying the intersection theory for twisted homology and cohomology groups, which arise from their Euler-type integral representations. In this article, we consider Appell-Lauricella's hypergeometric functions which are classical generalizations of Gauss' hypergeometric function. Especially, we focus on Lauricella's $F_A$ and $F_C$, and study them by using intersection theory. By evaluating some intersection numbers, we obtain quadratic relations between $F_A$ or $F_C$ as a consequence of the twisted period relations.