On a morphism of compactifications of moduli schemes of vector bundes

TL;DR

This paper constructs a morphism between different compactifications of moduli schemes of semistable sheaves on surfaces, leading to a new understanding of their scheme structures and relationships.

Contribution

It introduces a morphism from the Gieseker-Maruyama functor to the functor of admissible semistable pairs, connecting different moduli scheme compactifications.

Findings

Morphism of nonreduced functors constructed

Moduli schemes with possibly nonreduced structures related

Focus on main components of moduli schemes

Abstract

A morphism of nonreduced Gieseker - Maruyama functor (of semistable coherent torsion-free sheaves) on a surface to the nonreduced functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. This leads to the morphism of moduli schemes with possibly nonreduced scheme structures. As usually, we consider subfunctors corresponding to main components of moduli schemes.