A Torelli theorem for the moduli space of Higgs bundles on a curve

2001/07/14 by Indranil Biswas, Biswas, Indranil, Tomás L. Gómez +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14C34 #msc:14D20

paper · pdf · doi:10.48550/arxiv.math/0107108

LaTeX2e (11 pages)

arxiv created 2001/07/14 · arxiv updated 2009/11/30

Abstract

Let X be a smooth projective complex curve, and let M be the moduli space of stable Higgs bundles on X (with genus g>1), with rank n and fixed determinant ξ, with n and deg(ξ) coprime. Let X' and ξ' be another such curve and line bundle, and M' the corresponding moduli space. We prove that if M and M' are isomorphic as algebraic varieties, then X and X' are isomorphic.

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