Flips of moduli of stable torsion free sheaves with $c_1=1$ on $\mathbb{P}^2$

TL;DR

This paper investigates how moduli spaces of stable torsion free sheaves on the projective plane change via flips, interpreted as wall-crossing phenomena in the context of stable modules over finite dimensional algebras, described through stratified Grassmann bundles.

Contribution

It introduces a novel perspective on flips of moduli schemes as wall-crossing phenomena, connecting geometric transformations with algebraic stability conditions.

Findings

Describes flips as stratified Grassmann bundles.

Links wall-crossing in sheaf moduli to stable module categories.

Provides a new geometric interpretation of moduli space transformations.

Abstract

We study flips of moduli schemes of stable torsion free sheaves as wall-crossing phenomena of moduli schemes of stable modules over certain finite dimensional algebra. They are described as stratified Grassmann bundles.