Haupt's theorem for strata of abelian differentials
Geometric Topology
2021-07-05 v3 Algebraic Geometry
Complex Variables
Abstract
Let S be a closed topological surface. Haupt's theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be realized by integration against a complex-valued 1-form that is holomorphic with respect to some complex structure on S. We prove a refinement of this theorem that takes into account the divisor data of the 1-form.
Cite
@article{arxiv.2002.12901,
title = {Haupt's theorem for strata of abelian differentials},
author = {Matt Bainbridge and Chris Johnson and Chris Judge and Insung Park},
journal= {arXiv preprint arXiv:2002.12901},
year = {2021}
}