Hodge structures of the moduli spaces of pairs

2009/04/12 by Vicente Muñoz, Muñoz, Vicente
Mathematics · #14D20 #14F45 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0904.1842

openalex publication_date 2009/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Let X be a smooth projective curve of genus g≥ 2 over the complex numbers. Fix n≥ 2, and an integer d. A pair (E,ϕ) over X consists of an algebraic vector bundle E of rank n and degree d over X and a section ϕ. There is a concept of stability for pairs which depends on a real parameter τ. Let M_τ(n,d) be the moduli space of τ-semistable pairs of rank n and degree d over X. We prove that the cohomology groups of M_τ(n,d) are Hodge structures isomorphic to direct summands of tensor products of the Hodge structure H¹(X). This implies a similar result for the moduli spaces of stable vector bundles over X.

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