an:06728887
Zbl 1453.14106
Zhou, Jie
GKZ hypergeometric series for the Hesse pencil, chain integrals and orbifold singularities
EN
SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 030, 32 p. (2017).
00362559
2017
j
14J33 14Q05 30F30 34M35 14D07 14H52
GKZ system; chain integral; orbifold singularity; Hesse pencil
Summary: The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral, chain integral on the elliptic curve, limit of a period of a certain compact Calabi-Yau threefold geometry, etc. We also highlight the role played by the orbifold singularity on the moduli space and its relation to the GKZ system.