Linear series on curves: stability and Clifford index

Details Linear series on curves: stability and Clifford index Linear series on curves: stability and Clifford index

2011-11-01

arxiv.org/abs/1111.0304v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

We study concepts of stabilities associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the associated Dual Span Bundle and linear stability. Our result implies a stability condition related to the Clifford index of the curve. Furthermore, in some of the cases, we prove that a stronger stability holds: cohomological stability. Eventually using our results we obtain stable vector bundles of integral slope 3, and prove that they admit theta-divisors.

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