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

Let ${\text{cM}}_r$ 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 ${\text{cB}}_r\subset {\text{cM}}_r$ of the linear system of the determinant line bundle $\text{cL}$ over ${\text{cM}}_r$, i.e., the set of semi-stable rank-$r$ vector bundles without theta divisor. We construct base points in ${\text{cB}}_{g+2}$ over any curve $C$, and base points in ${\text{cB}}_4$ over any hyperelliptic curve.