Tau function and moduli of meromorphic forms on algebraic curves
Algebraic Geometry
2024-02-01 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We study the moduli space of meromorphic 1-forms on complex algebraic curves having at most simple poles with fixed nonzero residues. We interpret the Bergman tau function on this moduli space as a section of a line bundle and study its asymptotic behavior near the boundary and the locus of forms with non-simple zeros. As an application, we decompose the projection of this locus to the moduli space of curves into a linear combination of standard generators of the rational Picard group with explicit coefficients that depend on the residues.
Cite
@article{arxiv.2303.12244,
title = {Tau function and moduli of meromorphic forms on algebraic curves},
author = {Dmitry Korotkin and Peter Zograf},
journal= {arXiv preprint arXiv:2303.12244},
year = {2024}
}