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

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

2006-07-14

arxiv.org/abs/math/0607338v1

Mathematics

Algebraic Geometry

14 pages, LaTeX

Scientific paper

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 Poincar\'e 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.

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