We study concepts of stability associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the asso- ciated dual span bundle and linear stability. Our results imply that stability of the dual span holds under a hypothesis related to the Clifford index of the curve. Furthermore, in some of the cases, we prove that a stronger stability holds: cohomological stability. Finally, using our results we obtain stable vector bundles of slope 3, and prove that they admit theta-divisors.

Linear series on curves: stability and Clifford index

STOPPINO, LIDIA
2012-01-01

Abstract

We study concepts of stability associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the asso- ciated dual span bundle and linear stability. Our results imply that stability of the dual span holds under a hypothesis related to the Clifford index of the curve. Furthermore, in some of the cases, we prove that a stronger stability holds: cohomological stability. Finally, using our results we obtain stable vector bundles of slope 3, and prove that they admit theta-divisors.
2012
Slope Stability, Linear Stability, Cohomological Stability, Clifford Index, Dual Span Bundles, Linear Series, Butler's Conjecture.
Mistretta, E. C.; Stoppino, Lidia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1791985
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