Compactification of the moduli space of minimal instantons on the Fano threefold $V_4$

TL;DR

This paper establishes an isomorphism between the moduli space of certain semi-stable sheaves on a Fano threefold and vector bundles on a genus 2 curve, providing a smooth compactification of Ulrich bundle moduli.

Contribution

It introduces a natural smooth compactification of the moduli space of rank 2 Ulrich bundles on the Fano threefold V_4 by relating it to vector bundles on a genus 2 curve.

Findings

Moduli space of semi-stable sheaves is isomorphic to that of vector bundles on a genus 2 curve.

Provides a smooth compactification of the moduli space of Ulrich bundles.

Establishes a geometric correspondence between sheaves on V_4 and bundles on a curve.

Abstract

We study semi-stable sheaves of rank $2$ with Chern class $c_1=0$, $c_2=2$ and $c_3=0$ on the Fano 3-folds $V_4$ of Picard number $1$, degree $4$ and index $2$. We show the moduli space of such sheaves is isomorphic to the moduli space of semi-stable rank $2$ even degree vector bundles on a genus $2$ curve. This provides a natural smooth compatification of the moduli space of Ulrich bundles of rank $2$ on $V_4$.