Revista Matemática Iberoamericana
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Published online: 2015-07-16
A note on theta divisors of stable bundlesSonia Brivio (1) Università degli Studi di Pavia, Italy
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 $C$.
Keywords: Vector bundles
Brivio Sonia: A note on theta divisors of stable bundles. Rev. Mat. Iberoamericana 31 (2015), 601-608. doi: 10.4171/RMI/846