Projective moduli space of semistable principal sheaves for a reductive group

TL;DR

This paper introduces a new concept of principal G-sheaves on smooth projective varieties, defines semistability for them, and constructs a projective moduli space as a compactification of principal G-bundles.

Contribution

It generalizes principal G-bundles to principal G-sheaves and constructs their moduli space, providing a natural compactification.

Findings

Defined principal G-sheaves as a generalization of G-bundles

Constructed the projective moduli space of semistable principal G-sheaves

Provided a natural compactification of the moduli space of G-bundles

Abstract

Let X be a smooth projective complex variety, and let G be an algebraic reductive complex group. We define the notion of principal G-sheaf, that generalises the notion of principal G-bundle. Then we define a notion of semistability, and construct the projective moduli space of semistable principal G-sheaves on X. This is a natural compactification of the moduli space of principal G-bundles. This is the announcement note presented by the second author in the conference held at Catania (11-13 April 2001), dedicated to the 60th birthday of Silvio Greco. Detailed proofs will appear elsewhere.