Moduli spaces of coherent systems of small slope on algebraic curves

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

Published 2007-07-06, updated 2007-12-10Version 2

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 $\alpha$. 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.