Ulrich bundles on double covers of projective spaces

Abstract

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

Proof of Theorem 1.1 revised. 24 pages