A note on theta divisors of stable bundles

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