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# Mathematical Research Letters

## Volume 15 (2008)

### Number 4

### On the base locus of the linear system of generalized theta functions

Pages: 699 – 703

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n4.a8

#### Author

#### Abstract

Let $\cM_r$ 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 $\cB_r \subset \cM_r$ of the linear system of the determinant line bundle $\cL$ over $\cM_r$, i.e., the set of semi-stable rank-$r$ vector bundles without theta divisor. We construct base points in $\cB_{g+2}$ over any curve $C$, and base points in $\cB_4$ over any hyperelliptic curve.