Existence of Ulrich bundles on every projective variety

Determine whether every projective variety admits an Ulrich bundle.

Background

Ulrich bundles are a distinguished subclass of ACM bundles with maximally generated modules and desirable cohomological properties. The existence problem—whether every projective variety supports an Ulrich bundle—has become a central open challenge, with extensive literature summarized in the referenced survey and monographs.

The authors specifically identify this as an ongoing conjecture and note it as a next challenge within the broader paper of ACM and Ulrich bundles.