On the Base Locus of the Linear System of Generalized Theta Functions

Let Mr denote the moduli space of semi-stable rank-r vector bundles with trivial determinant over a smooth projective curve C of genus g. In this paper we study the base locus Br ⊂ Mr of the linear system of the determinant line bundle L over Mr, i.e., the set of semi-stable rank-r vector bundles without theta divisor. We construct base points in Bg+2 over any curve C, and base points in B4 over any hyperelliptic curve.