Torsion Free Sheaves on Cuspidal Curves

TL;DR

This paper investigates torsion free sheaves on singular projective curves with cusps, adapting existing structures from nodal cases to describe these sheaves via triples on the normalization.

Contribution

It extends Seshadri's framework from nodal to cuspidal curves, providing a new description of torsion free sheaves on such singular curves.

Findings

Describes torsion free sheaves on cuspidal curves using triples on the normalization.

Adapts Seshadri's structure from nodal to cuspidal singularities.

Provides a classification framework for sheaves on integral projective curves with cusps.

Abstract

We study torsion free sheaves on integral projective curves with at most ordinary cusps as singularities. Adjusting Seshadri's structure from the nodal case to this one, we describe these sheaves by means of a triple defined in the normalization of the curve.