Moduli of sheaves and deformation to the normal cone

2025/11/21 by Zhao, Yifan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2511.17700

openalex publication_date 2025/11/21 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

Given a closed immersion between arbitrary smooth complex projective varieties, we prove that the two operations: (1) taking the moduli space of stable sheaves, and (2) taking the deformation to the normal cone, commute in a precise sense. In the case of curves inside symplectic surfaces, previously studied by Donagi-Ein-Lazarsfeld, the corresponding deformation to the normal cone space is an open subset of the relative moduli space of sheaves. As an application, we show generalized Kummer varieties degenerate to natural symplectic subvarieties of the Hitchin system for curves of genus at least 2.

Citations

• O'Grady spaces and symplectic resolution of moduli spaces of Higgs bundles
• P=W conjectures for character varieties with symplectic resolution
• Hitchin fibrations, abelian surfaces, and the P=W conjecture
• Topology of Hitchin systems and Hodge theory of character varieties: the case A₁
• On the Euler Characteristic of Generalized Kummer Varieties
• Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles

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