GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
Classical Analysis and ODEs
2017-05-23 v4 Mathematical Physics
Complex Variables
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1606.08352,
title = {GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities},
author = {Jie Zhou},
journal= {arXiv preprint arXiv:1606.08352},
year = {2017}
}