Nodal curves and polarizations with good properties

Abstract

In this paper we deal with polarizations on a nodal curve $C$ with smooth components. Our aim is to study and characterize a class of polarizations, which we call "good", for which depth one sheaves on $C$ reflect some properties that hold for vector bundles on smooth curves. We will concentrate, in particular, on the relation between the $\underline{w}$-stability of ${\mathcal{O}}_C$ and the goodness of $\underline{w}$. We prove that these two concepts agree when $C$ is of compact type and we conjecture that the same should hold for all nodal curves.

22 pages. New version has some changes and corrections. To appear on "Revista Matemática Complutense"

References in corpus (4)

• On kernel bundles over reducible curves with a node
• Genus 2 curves and generalized theta divisors
• Coherent systems on curves of compact type
• On vector bundles over reducible curves with a node

Cited by in corpus (1)

• Coherent systems and BGN extensions on nodal reducible curves