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Relative Log-Symplectic structure on a semi-stable degeneration of moduli of Higgs bundles

2021/01/18 by Sourav Das, Das, Sourav
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2101.07056

openalex publication_date 2021/01/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In a recent paper \cite3, a semi-stable degeneration of moduli space of Higgs bundles on a curve has been constructed. In this paper, we show that there is a relative log-symplectic form on this degeneration, whose restriction to the generic fibre is the classical symplectic form discovered by Hitchin. We compute the Poisson ranks at every point and describe the symplectic foliation on the closed fibre. We also show that the closed fibre, which is a variety with normal crossing singularities, acquires a structure of an algebraically completely integrable system.

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