Moduli spaces of SL(r)-bundles on singular irreducible curves

2003/03/17 by Xiaotao Sun, Sun, Xiaotao
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0303198

19 pages

arxiv created 2003/03/17 · openalex publication_date 2003/03/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a stable irreducible curve X and a torsion free sheaf L on X of rank one and degree d, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed subset \Cal U_X(r,L) in the moduli space of semistable torsion free sheaves of rank r and degree d on X. We prove that \Cal U_X(r,L) is irreducible, when a smooth curve Y specializes to X and a line bundle \Cal L on Y specializes to L, the specialization of moduli space of semistable rank r vector bundles on Y with fixed determinant \Cal L has underlying set \Cal U_X(r,L). For rank 2 and 3, we show that there is a Cohen-Macaulay closed subscheme in the Gieseker space which represents a suitable moduli functor and has good specialization property.

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