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

Georg Hein
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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.

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Georg Hein. 2006-07-14. Raynaud's vector bundles and base points of the generalized Theta divisor. https://arxiv.org/abs/math/0607338

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