Analytic moduli spaces of simple sheaves on families of integral curves

TL;DR

This paper establishes the existence of fine moduli spaces for simple coherent sheaves on families of irreducible curves, utilizing a universal bound on Castelnuovo-Mumford regularity to prove the result.

Contribution

It introduces a universal upper bound on Castelnuovo-Mumford regularity, enabling the construction of fine moduli spaces for simple sheaves on families of curves.

Findings

Existence of fine moduli spaces for simple sheaves on irreducible curves.

Universal bound on Castelnuovo-Mumford regularity.

Method applicable to families of integral curves.

Abstract

We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo-Mumford regularity of such sheaves, which we provide.