# Moduli spaces of rank 2 instanton sheaves on the projective space

## TL;DR

This paper classifies all rank 2 instanton sheaves with second Chern class up to 4 on projective 3-space, describing their moduli space components and analyzing related stable sheaf moduli spaces.

## Contribution

It provides a complete classification of instanton sheaves with low second Chern class and describes the irreducible components of their moduli spaces, including the study of related stable sheaf moduli.

## Key findings

- Classified all instanton sheaves with c2 ≤ 4 on P^3.
- Described all irreducible components of their moduli spaces.
- Analyzed the moduli space of stable sheaves with Hilbert polynomial d·t for d ≤ 4.

## Abstract

We study the irreducible components of the moduli space of instanton sheaves on $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we classify all instanton sheaves with $c_2(E)\le4$, describing all the irreducible components of their moduli space. A key ingredient for our argument is the study of the moduli space ${\mathcal T}(d)$ of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $P(t)=d\cdot t$, which contains, as an open subset, the moduli space of rank 0 instanton sheaves of multiplicity $d$; we describe all the irreducible components of ${\mathcal T}(d)$ for $d\le4$.