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

Christian Pauly (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Géométrie algébrique [math.AG]

Christian Pauly. On the base locus of the linear system of generalized theta functions. 2008. ⟨hal-00164700v2⟩