Ulrich Bundles on Veronese surfaces

TL;DR

This paper classifies Ulrich bundles on Veronese surfaces, showing they have specific resolutions, and extends the results to prove the existence of stable Ulrich bundles on projective spaces with various polarizations.

Contribution

It provides a complete resolution classification for Ulrich bundles on Veronese surfaces and establishes existence results for stable Ulrich bundles on projective spaces.

Findings

Ulrich bundles on Veronese surfaces have resolutions in terms of trivial bundle twists.

Existence of stable Ulrich bundles on projective spaces with arbitrary polarization.

Classification facilitates understanding of Ulrich bundle structures.

Abstract

We prove that every Ulrich bundle on the Veronese surface has a resolution in terms of twists of the trivial bundle over $\mathbb{P}^{2}$. Using this classification, we prove existence results for stable Ulrich bundles over $\mathbb{P}^{k}$ with respect to an arbitrary polarization $dH$.