Ulrich ranks of Veronese varieties and equivariant instantons

TL;DR

This paper constructs and classifies Ulrich bundles on Veronese threefolds by deforming symmetric squares of equivariant instanton bundles, confirming a conjecture and advancing understanding of these geometric objects.

Contribution

It introduces a method to construct Ulrich bundles on Veronese threefolds and classifies their ranks, proving a conjecture by Costa and Miró-Roig.

Findings

Ulrich bundles on Veronese threefolds are constructed as deformations of symmetric squares of instanton bundles.

The classification of ranks of Ulrich bundles on these varieties is achieved.

A conjecture by Costa and Miró-Roig is proven.

Abstract

We construct Ulrich bundles on Veronese threefolds of arbitrary degree as generic deformations of symmetric squares of equivariant instanton bundles on the projective space, thus classifying the rank of Ulrich bundles on such varieties and proving a conjecture of Costa and Mir{\'o}-Roig.