Moduli spaces of Ulrich bundles on the Fano 3-fold $V_5$

TL;DR

This paper investigates the structure of moduli spaces of Ulrich bundles on the Fano 3-fold V_5, revealing their connection to quiver representation spaces and providing a detailed geometric description.

Contribution

It establishes an explicit isomorphism between the moduli space of stable Ulrich bundles on V_5 and a smooth open subset of a quiver representation moduli space, extending understanding of bundle moduli on Fano threefolds.

Findings

Moduli space of stable Ulrich bundles is smooth and of dimension r^2+1.

Identifies the moduli space with an open subset of Kronecker quiver representations.

Provides a geometric description linking Ulrich bundles to quiver theory.

Abstract

We study moduli spaces of Ulrich bundles of rank $r \geq 2$ on the Fano 3-fold $V_5$ of Picard number 1, degree 5 and index 2. We prove that the moduli space of stable Ulrich bundles of rank $r$ on $V_5$ can be identified with a smooth $(r^2+1)$-dimensional open subset of the moduli space of stable quiver representations with dimension vector $(r, r)$ of the Kronecker quiver with 2 vertices and 3 arrows.