Ulrich bundles on double covers of projective spaces

TL;DR

This paper proves the existence of Ulrich bundles on all smooth double covers of projective spaces, including rank two bundles on surfaces, expanding the understanding of vector bundles in algebraic geometry.

Contribution

It establishes the existence of Ulrich bundles on any smooth double cover of projective space, with a specific focus on rank two bundles for surfaces.

Findings

Ulrich bundles exist on all smooth double covers of projective spaces.

Rank two Ulrich bundles are constructed on double covers of surfaces.

The results extend the class of varieties known to admit Ulrich bundles.

Abstract

In this article, we prove that any smooth projective variety $X$ which is a double cover of the projective space $\mathbb{P}^n$ ($n\geq 2$) admits an Ulrich bundle. When $n=2$, we show that on any such $X$, there is an Ulrich bundle of rank two.