GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities

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.

References in corpus (6)

• N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
• On Rationally Parametrized Modular Equations
• Holomorphic N=1 Special Geometry of Open--Closed Type II Strings
• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• LG/CY Correspondence for Elliptic Orbifold Curves via Modularity
• Mirror Symmetry for Plane Cubics Revisited