The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobian

1998/05/07 by B. van Geemen, van Geemen, B., Elham Izadi +2 · 2 citations
Mathematics · #14H42 (Secondary) #14H60 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14H42 #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/9805037

33 pages, AMS-Latex

arxiv created 1998/05/07 · openalex publication_date 1998/05/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We complete the proof of the fact that the moduli space of rank two bundles with trivial determinant embeds into the linear system of divisors on Pic^g-1C which are linearly equivalent to 2Θ. The embedded tangent space at a semi-stable non-stable bundle ξ⊕ξ^-1, where ξ is a degree zero line bundle, is shown to consist of those divisors in |2Θ| which contain Sing(Θ_ξ) where Θ_ξ is the translate of Θ by ξ. We also obtain geometrical results on the structure of this tangent space.

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