Spaces of Abelian Differentials and Hitchin’s Spectral Covers-Reference-Cited by-同舟云学术

Spaces of Abelian Differentials and Hitchin’s Spectral Covers

Published:2019-07-20 Issue:15 Volume:2021 Page:11246-11269
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bertola M¹,Korotkin D²

Affiliation:

1. Department of Mathematics and Statistics, Concordia University 1455 de Maisonneuve W., Montréal, Québec H3G IM8, Canada

2. SISSA/ISAS, Area of Mathematics via Bonomea 265, Trieste, Italy

Abstract

Abstract Using the embedding of the moduli space of generalized $GL(n)$ Hitchin’s spectral covers to the moduli space of meromorphic Abelian differentials we study the variational formulæ of the period matrix, the canonical bidifferential, the prime form and the Bergman tau function. This leads to residue formulæ which generalize the Donagi–Markman formula for variations of the period matrix. The computation of second derivatives of the period matrix reproduces the formula derived in [2] using the framework of topological recursion.

Funder

Natural Sciences and Engineering Research Council of Canada

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/15/11246/39457989/rnz142.pdf

Reference19 articles.

1. The Geometry and Physics of Knots

2. Second and third order observables of the two-matrix model;Bertola;J. High Energy Phys.,2003

3. Symplectic geometry of the moduli space of projective structures in homological coordinates;Bertola;Invent. Math.,2017

4. Hodge and Prym tau functions, Jenkins–Strebel differentials and combinatorial model of ${\mathcal{M}}_{g,n}$;Bertola

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