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 Θ<inf>E</inf>, whose singular locus has dimension g - 4. If C is non-hyperelliptic of genus 3, then actually Θ<inf>E</inf> is smooth and irreducible for a general stable vector bundle E with integer slope on C.
Brivio, S. (2015). A note on theta divisors of stable bundles. REVISTA MATEMATICA IBEROAMERICANA, 31(2), 601-608 [10.4171/rmi/846].
A note on theta divisors of stable bundles
BRIVIO, SONIA
Primo
2015
Abstract
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 Θ
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