Mirror symmetry for parabolic Higgs bundles via \(p\)-adic integration

DOI10.1016/j.aim.2024.109616arXiv2302.02817OpenAlexW4392936203MaRDI QIDQ6126744

Shiyu Shen

Publication date: 10 April 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.02817

zbMATH Keywords

mirror symmetryHiggs bundles\(p\)aAdic integration

Mathematics Subject Classification ID

Surfaces and higher-dimensional varieties (14Jxx) Curves in algebraic geometry (14Hxx) Families, fibrations in algebraic geometry (14Dxx)

Cites Work

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• Langlands duality for Hitchin systems
• Mirror symmetry for moduli spaces of Higgs bundles via \(p\)-adic integration
• Geometric Langlands correspondence for \({\mathcal D}\)-modules in prime characteristic: the \(\mathrm{GL}(n)\) case
• Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz.
• Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
• Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves
• Mirror symmetry, Langlands duality, and the Hitchin system
• The wild McKay correspondence and \(p\)-adic measures
• Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
• Topological mirror symmetry for parabolic Higgs bundles
• Toroidal Algebraic Groups
• Geometric stabilisation via $p$-adic integration
• Endoscopic decompositions and the Hausel–Thaddeus conjecture
• The Self-Duality Equations on a Riemann Surface
• Spectral curves and the generalised theta divisor.
• Twisted Bundles and Admissible Covers
• On the image of the parabolic Hitchin map
• Torus fibrations, gerbes, and duality

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