Ulrich Bundles on Quartic Surfaces with Picard Number 1

TL;DR

This paper proves the existence of stable Ulrich bundles of all even ranks on smooth quartic surfaces in projective 3-space with Picard number one, expanding understanding of vector bundles on such surfaces.

Contribution

It establishes the existence of stable Ulrich bundles of every even rank on a specific class of quartic surfaces, a new result in the study of vector bundles on algebraic surfaces.

Findings

Stable Ulrich bundles of all even ranks exist on the given surfaces.

The result applies to smooth quartic surfaces with Picard number 1.

It advances the classification of Ulrich bundles on algebraic surfaces.

Abstract

In this note, we prove that there exist stable Ulrich bundles of every even rank on a smooth quartic surface $X \subset \mathbb{P}^3$ with Picard number 1.