Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero
Algebraic Geometry
2021-09-03 v1 Complex Variables
Number Theory
Abstract
We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomolgy with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields.
Keywords
Cite
@article{arxiv.2109.00587,
title = {Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero},
author = {Jin Cao and Hossein Movasati and Roberto Villaflor Loyola},
journal= {arXiv preprint arXiv:2109.00587},
year = {2021}
}