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arXiv · 2004.02529

Coherent systems on curves of compact type

Sonia Brivio·Filippo F. Favale
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Abstract

Let $C$ be a polarized nodal curve of compact type. In this paper we study coherent systems $(E,V)$ on $C$ given by a depth one sheaf $E$ having rank $r$ on each irreducible component of $C$ and a subspace $V \subset H^0(E)$ of dimension $k$. Moduli spaces of stable coherent systems have been introduced by King and Newstead and depend on a real parameter $\alpha$. We show that when $k \geq r$, these moduli spaces coincide for $\alpha$ big enough. Then we deal with the case $k=r+1$: when the degrees of the restrictions of $E$ are big enough we are able to describe an irreducible component of this moduli space by using the dual span construction.

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Sonia Brivio, Filippo F. Favale. 2020-04-06. Coherent systems on curves of compact type. https://doi.org/10.1016/j.geomphys.2020.103850

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