On Clifford dimension for singular curves

TL;DR

This paper investigates the Clifford dimension of integral curves by extending the Clifford index to torsion-free sheaves, deriving formulas for monomial curves, and analyzing the case when the Clifford dimension equals 2.

Contribution

It introduces an extension of the Clifford index to torsion-free sheaves and provides combinatorial formulas for monomial curves, advancing understanding of Clifford dimension for singular curves.

Findings

Extended Clifford index to torsion-free sheaves

Derived combinatorial formulas for monomial curves

Analyzed the case of Clifford dimension 2

Abstract

We study the Clifford dimension of an integral curve. To do so, we extend the notion of Clifford index, allowing torsion-free sheaves on its computation. We derive results for arbitrary curves, and then focus on the monomial case. In this context, we obtain combinatorial formulae for the Clifford index and apply them to the case of Clifford dimension $2$.