A note on theta divisors of stable bundles

Abstract

Let $C$ be a smooth complex irreducible projective curve of genus $g \geq 3$. We show that if $C$ is a Petri curve with $g \geq 4$, a general stable vector bundle $E$ on $C$, with integer slope, admits an irreducible and reduced theta divisor $\Theta\_E$, whose singular locus has dimension $g-4$. If $C$ is non-hyperelliptic of genus $3$, then actually $\Theta\_E$ is smooth and irreducible for a general stable vector bundle $E$ with integer slope on $C$.