Non-emptiness of moduli spaces of coherent systems

Details Non-emptiness of moduli spaces of coherent systems Non-emptiness of moduli spaces of coherent systems

2004-12-14

arxiv.org/abs/math/0412285v2

Mathematics

Algebraic Geometry

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

Scientific paper

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

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