Non-emptiness of moduli spaces of coherent systems

Abstract

Let X be a general smooth projective algebraic curve of genus g>1. We prove that the moduli space G(α:n,d,k) of $\alpha$-stable coherent systems of type (n,d,k) over X is empty if k>n and the Brill-Noether number is negative. Moreover, if the Brill-Noether number is positive and <g and for some $\alpha >0$, G(α:n,d,k) is non-empty G(α:n,d,k) is non-empty for all $\alpha >0$ and G(α:n,d,k)= G(α':n,d,k) for all $\alpha ,{\alpha }^{\prime }>0$ and the generic element is generated.

Revised version. To appear in Internat. J. Math 22 pages, AMS-Tex

References in corpus (1)

• Geography of Brill-Noether loci for small slopes