# Instanton sheaves and representations of quivers

## TL;DR

This paper explores the moduli space of rank 2 instanton sheaves on projective 3-space using quiver representations, revealing stability conditions and wall-chamber structures that suggest new compactifications.

## Contribution

It introduces a quiver representation framework for instanton sheaves, analyzes stability conditions, and describes the wall-chamber decomposition for low-charge cases.

## Key findings

- Existence of a stability parameter for each instanton sheaf
- Wall-and-chamber decomposition of stability parameters
- Complete description for charge 1 instantons

## Abstract

We study the moduli space of rank 2 instanton sheaves on $\p3$ in terms of representations of a quiver consisting of 3 vertices and 4 arrows between two pairs of vertices. Aiming at an alternative compactification for the moduli space of instanton sheaves, we show that for each rank 2 instanton sheaf, there is a stability parameter $\theta$ for which the corresponding quiver representation is $\theta$-stable (in the sense of King), and that the space of stability parameters has a non trivial wall-and-chamber decomposition. Looking more closely at instantons of low charge, we prove that there are stability parameters with respect to which every representation corresponding to a rank 2 instanton sheaf of charge 2 is stable, and provide a complete description of the wall-and-chamber decomposition for representation corresponding to a rank 2 instanton sheaf of charge 1.