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 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.