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(\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 <g and for some $\alpha >0$, 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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- December 2004
- DOI:
- arXiv:
- arXiv:math/0412285
- Bibcode:
- 2004math.....12285B
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14H60;
- 14J60
- E-Print:
- Revised version. To appear in Internat. J. Math 22 pages, AMS-Tex