Pfaffian of Appell's hypergeometric system $F_4$ in terms of the intersection form of twisted cohomology groups

Abstract

We study a Pfaffian of the system of differential equations annihilating Appell's hypergeometric series $F_4(a,b,c;x)$ by twisted cohomology groups associated with integrals representing solutions to this system. We simplify its connection matrix by the pull-back under a double cover of the complement of the singular locus. We express the simplified connection matrix in terms of the intersection form of the twisted cohomology groups.

23 pages, 1 figure

References in corpus (1)

• Pfaffian of Lauricella's hypergeometric system $F_A$