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Mathematical Physics

arXiv:1812.05789 (math-ph)
[Submitted on 14 Dec 2018 (v1), last revised 27 Jun 2019 (this version, v2)]

Title:Spaces of abelian differentials and Hitchin's spectral covers

Authors:Marco Bertola, Dmitry Korotkin
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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 formulae of the period matrix, the canonical bidifferential, the prime form and the Bergman tau function. This leads to residue formulae which generalize the Donagi-Markman formula for variations of the period matrix. Computation of second derivatives of the period matrix reproduces the formula derived by Baraglia and Zhenxi Huang using the framework of topological recursion.
Subjects: Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:1812.05789 [math-ph]
  (or arXiv:1812.05789v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1812.05789

Submission history

From: Dmitry Korotkin [view email]
[v1] Fri, 14 Dec 2018 05:26:00 UTC (19 KB)
[v2] Thu, 27 Jun 2019 02:03:02 UTC (20 KB)
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