A desingularization of the moduli space of rank 2 Higgs bundles over a\n curve

2013/10/29 by Sang‐Bum Yoo, Yoo, Sang-Bum
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1310.7809

openalex publication_date 2013/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth complex projective curve of genus g\≥ 3. Let\n\M₂ be the moduli space of semistable rank 2 Higgs bundles with\ntrivial determinant over X. We construct a desingularization \S of\n\M₂ as a closed subvariety of a moduli space. We prove that\n\S is a nonsingular variety containing the stable locus of\n\M₂ as an open dense subvariety. On the other hand, there is another\ndesingularization \K of \M₂ obtained from Kirwan's\nalgorithm. We show that \S can be obtained after two blow-downs of\n\K.\n

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