2017/01/25 by Andrea Tirelli, Tirelli, Andrea
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1701.07468
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the algebraic symplectic geometry of the singular moduli spaces of Higgs bundles of degree 0 and rank n on a compact Riemann surface X of genus g. In particular, we prove that such moduli spaces are symplectic singularities, in the sense of Beauville [Bea00], and admit a projective symplectic resolution if and only if g=1 or (g, n)=(2,2). These results are an application of a recent paper by Bellamy and Schedler [BS16] via the so-called Isosingularity Theorem.