Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 001, 10 pages      arXiv:2108.01419      https://doi.org/10.3842/SIGMA.2022.001
Contribution to the Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan

Tau Function and Moduli of Meromorphic Quadratic Differentials

Dmitry Korotkin ab and Peter Zograf bc
a) Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve West, Montreal, H3G 1M8 Quebec, Canada
b) Euler International Mathematical Institute, Pesochnaja nab. 10, Saint Petersburg, 197022 Russia
c) Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O. 29, Saint Petersburg, 199178 Russia

Received August 09, 2021, in final form December 28, 2021; Published online January 03, 2022; References for Lemma 1.1 added January 09, 2022

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.

Key words: quadratic differentials; tau function; moduli spaces.

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