On a new compactification of moduli of vector bundles on a surface, IV: Nonreduced moduli

TL;DR

This paper constructs a nonreduced projective moduli scheme for semistable admissible pairs on a surface, relating it to the reduced scheme and showing an open subset is isomorphic to the moduli of semistable vector bundles.

Contribution

It introduces a new nonreduced moduli scheme for admissible pairs and establishes its connection with the reduced moduli scheme, including an isomorphism with vector bundle moduli.

Findings

Nonreduced moduli scheme constructed for semistable admissible pairs.

Relation established between nonreduced and reduced moduli schemes.

Open subscheme isomorphic to moduli of semistable vector bundles.

Abstract

The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced moduli scheme contains an open subscheme which is isomorphic to moduli scheme of semistable vector bundles.