Holomorphic symplectic manifolds from semistable Higgs bundles

2024/06/01 by Roland Abuaf, Abuaf, Roland, Riccardo Carini +1
Mathematics · #14D20 #14J42 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2406.00395

openalex publication_date 2024/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M_C(2, 0) be the moduli space of semistable rank two and degree zero Higgs bundles on a smooth complex hyperelliptic curve C of genus three. We prove that the quotient of M_C(2, 0) by a twisted version of the hyperelliptic involution is an 18-dimensional holomorphic symplectic variety admitting a crepant resolution, whose local model was studied by Kaledin and Lehn to describe O'Grady's singularities. Similarly, by considering the moduli space of Higgs bundles with trivial determinant M_C(2, O_C)⊆ M_C(2, 0), we show that the quotient of M_C(2, O_C) by the hyperelliptic involution is a 12-dimensional holomorphic symplectic variety admitting a crepant resolution.

Related

• O'Grady spaces and symplectic resolution of moduli spaces of Higgs bundles
• Symplectic resolutions of moduli spaces of G-Higgs bundles
• Symplectic resolutions for Higgs moduli spaces
• A desingularization of the moduli space of rank 2 Higgs bundles over a curve
• Geometry of the moduli space of Higgs bundles