JournalsprimsVol. 52, No. 2pp. 223–247

Pfaffian of Appell's Hypergeometric System F4\mathcal F_4 in Terms of the Intersection Form of Twisted Cohomology Groups

  • Yoshiaki Goto

    Kobe University, Japan
  • Jyoichi Kaneko

    University of the Ryukyus, Okinawa, Japan
  • Keiji Matsumoto

    Hokkaido University, Sapporo, Japan
Pfaffian of Appell's Hypergeometric System $\mathcal F_4$ in Terms of the Intersection Form of Twisted Cohomology Groups cover
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Abstract

We study a Pfaffian of Appell's hypergeometric system F4(a,b,c)\mathcal F_4 (a,b,c) of differential equations by twisted cohomology groups associated with Euler type integrals representing solutions. 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 between the twisted cohomology groups.

Cite this article

Yoshiaki Goto, Jyoichi Kaneko, Keiji Matsumoto, Pfaffian of Appell's Hypergeometric System F4\mathcal F_4 in Terms of the Intersection Form of Twisted Cohomology Groups. Publ. Res. Inst. Math. Sci. 52 (2016), no. 2, pp. 223–247

DOI 10.4171/PRIMS/179