Revista Matemática Iberoamericana


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Volume 31, Issue 2, 2015, pp. 601–608
DOI: 10.4171/RMI/846

Published online: 2015-07-16

A note on theta divisors of stable bundles

Sonia Brivio[1]

(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