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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.