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arXiv · 0707.0983

Moduli spaces of coherent systems of small slope on algebraic curves

S. B. Bradlow·O. Garcia-Prada·V. Mercat·V. Munoz·P. E. Newstead
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Abstract

Let $C$ be an algebraic curve of genus $g\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $α$. We study the geometry of the moduli space of coherent systems for $0<d\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness.

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S. B. Bradlow, O. Garcia-Prada, V. Mercat, V. Munoz, P. E. Newstead. 2007-12-10. Moduli spaces of coherent systems of small slope on algebraic curves. https://arxiv.org/abs/0707.0983

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