Raynaud's vector bundles and base points of the generalized Theta divisor

2006/07/14 by Georg Hein, Hein, Georg
Mathematics · #14D20 (Primary) 14F17 #18E30 (Secondary) #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.math/0607338

openalex publication_date 2006/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study base points of the generalized Theta-divisor on the moduli space of vector bundles on a smooth algebraic curve X of genus g defined over an algebraically closed field. To do so, we use the derived categories D(Pic(X)), D(Jac(X)), and the equivalence between them given by the Fourier-Mukai transform coming from the Poincaré bundle. The vector bundles P(m) on the curve X defined by Raynaud play a central role in this description. Indeed, we show that a vector bundle E is a base point of the generalized Theta-divisor, if and only if there exists a nontrivial homomorphism P(rk(E)g+1) --> E.

Citations

• Vector bundles on curves and generalized theta functions: recent results and open problems
• Vector Bundles Over an Elliptic Curve

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