An introduction to Ulrich bundles

TL;DR

This paper introduces Ulrich bundles, discusses their fundamental properties, and explores their existence on various varieties, showing positive results for certain surfaces and threefolds using Serre construction.

Contribution

It provides new existence results for Ulrich bundles on specific surfaces and threefolds via Serre construction, advancing understanding of their presence on smooth projective varieties.

Findings

Ulrich bundles are defined and their basic properties are recalled.

The existence problem for Ulrich bundles is addressed.

Serre construction yields positive existence results on certain surfaces and threefolds.

Abstract

After recalling the definition and basic properties of Ulrich bundles, we focus on the existence problem: does any smooth projective variety carry a Ulrich bundle? We show that the Serre construction provides a positive answer on certain surfaces and threefolds.