Tau Function and Moduli of Meromorphic Quadratic Differentials

TL;DR

This paper explores the use of Bergman tau functions to analyze the Picard group of moduli spaces of quadratic differentials with simple poles, extending previous work on holomorphic cases.

Contribution

It introduces a novel application of tau functions to the study of moduli spaces with poles, broadening the scope of prior results.

Findings

Generalization of tau function applications to meromorphic quadratic differentials

New insights into the Picard group structure of these moduli spaces

Extension of previous holomorphic differential results

Abstract

The Bergman tau functions are applied to the study of the Picard group of moduli spaces of quadratic differentials with at most $n$ simple poles on genus $g$ complex algebraic curves. This generalizes our previous results on moduli spaces of holomorphic quadratic differentials.