Duality Construction of Moduli Spaces

TL;DR

This paper introduces a dual moduli space for rank-2 coherent sheaves on algebraic surfaces, enabling a GIT-free construction and generalizing jumping lines through a finite Barth-morphism.

Contribution

It constructs a dual moduli space and a Barth-morphism, extending the understanding of moduli spaces without relying on GIT methods.

Findings

Existence of a dual moduli space for rank-2 sheaves.

Construction of a finite Barth-morphism generalizing jumping lines.

GIT-free approach to moduli space construction.

Abstract

We show for the moduli space of rank-2 coherent sheaves on an algebraic surface that there exists a 'dual' moduli space. This dual space allows a construction of the first one without using the GIT construction. Furthermore, we obtain a Barth-morphism, generalizing the concept of jumping lines. This morphism is by construction a finite morphism.