Pfaffian of Appell's hypergeometric system F4 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 F4(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.
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