Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$

TL;DR

This paper investigates the moduli space of certain rank 2 sheaves on the Fano threefold V_5, revealing a component isomorphic to projective 5-space and providing a natural compactification for minimal instantons and Ulrich bundles.

Contribution

It identifies a component of the moduli space of rank 2 sheaves on V_5 with a projective space and constructs a smooth compactification for minimal instantons and Ulrich bundles.

Findings

The moduli space has a component isomorphic to ^5.

Provides a natural smooth compactification of the moduli space.

Connects the moduli space to semistable quiver representations.

Abstract

We study semistable sheaves of rank $2$ with Chern classes $c_1=0$, $c_2=2$ and $c_3=0$ on the Fano 3-fold $V_5$ of Picard number $1$, degree $5$ and index $2$. We show that the moduli space of such sheaves has a component that is isomorphic to $\mathbb{P}^5$ by identifying it with the moduli space of semistable quiver representations. This provides a natural smooth compactification of the moduli space of minimal instantons, as well as Ulrich bundles of rank $2$ on $V_5$.