Spaces of Abelian Differentials and Hitchin’s Spectral Covers

DOI10.1093/imrn/rnz142zbMath1485.14044arXiv1812.05789OpenAlexW2963289182WikidataQ127745404 ScholiaQ127745404MaRDI QIDQ5068180

Marco Bertola, Dmitry Korotkin

Publication date: 5 April 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05789

zbMATH Keywords

Riemann surfacesmoduli spacesperiod matrixabelian differentialsBergman tau functiondeformation calculusHitchin's spectral covers

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Period matrices, variation of Hodge structure; degenerations (32G20) Families, moduli of curves (analytic) (14H15) Differentials on Riemann surfaces (30F30)

Related Items (4)

On generalized WKB expansion of monodromy generating function ⋮ Szegő kernel and symplectic aspects of spectral transform for extended spaces of rational matrices ⋮ Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion ⋮ Airy structures and deformations of curves in surfaces

Cites Work

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• Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula
• Tau function and moduli of differentials
• Special Kähler geometry of the Hitchin system and topological recursion
• The Self-Duality Equations on a Riemann Surface
• Kernel functions, analytic torsion, and moduli spaces
• Tau functions, Hodge classes, and discriminant loci on moduli spaces of Hitchin’s spectral covers
• Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles

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