Sur les conditions d'existence des faisceaux semi-stables sur les courbes multiples primitives

TL;DR

This paper establishes conditions for the (semi-)stability of torsion free sheaves on primitive multiple curves, demonstrating the non-emptiness of certain moduli spaces and analyzing quasi locally free sheaves of generic type.

Contribution

It provides new sufficient conditions for stability of sheaves on primitive multiple curves and explores the structure of their moduli spaces, especially for quasi locally free sheaves.

Findings

Conditions ensuring (semi-)stability of sheaves

Existence of non-empty moduli spaces of stable sheaves

Characterization of quasi locally free sheaves of generic type

Abstract

We give sufficient conditions for the (semi-)stability of torsion free sheaves on a primitive multiple curve. These conditions are used to prove that some moduli spaces of stable sheaves are not empty. We study mainly the quasi locally free sheaves of generic type (this includes the locally free sheaves). These sheaves are generic, i.e. for every moduli space of torsion free sheaves, the sheaves of this type correspond to an open subset of the moduli space.