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Non-emptiness of moduli spaces of coherent systems

L. Brambila-Paz
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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 $α$-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(α:n,d,k) is non-empty G(α:n,d,k) is non-empty for all $α>0$ and G(α:n,d,k)= G(α':n,d,k) for all $α,α'>0$ and the generic element is generated.

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L. Brambila-Paz. 2007-11-15. Non-emptiness of moduli spaces of coherent systems. https://arxiv.org/abs/math/0412285

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