Ulrich bundles on blowups

TL;DR

This paper constructs Ulrich bundles on blowups of varieties with existing Ulrich bundles, exploring their properties and relations to the original surfaces, under certain positivity conditions.

Contribution

It introduces a method to produce Ulrich bundles on blowups from those on the original variety, expanding the understanding of Ulrich bundles in algebraic geometry.

Findings

Ulrich bundles can be constructed on blowups under positivity assumptions.

The relation between Ulrich bundles on the original and blown-up surfaces is characterized.

Conditions for the existence of Ulrich bundles on blowups are established.

Abstract

We construct an Ulrich bundle on the blowup at a point when the original variety is embedded by a sufficiently positive linear system and carries an Ulrich bundle. In particular, we describe the relation between special Ulrich bundles on the blown-up surfaces and the original surfaces.