Ulrich bundles with $c_2(\mathcal E)^2=0$ and connectedness of Ulrich subvarieties

TL;DR

This paper classifies Ulrich bundles with zero second Chern class squared on high-dimensional varieties and explores the geometric constraints and connectedness properties of Ulrich subvarieties.

Contribution

It provides an almost complete classification of specific Ulrich bundles and investigates the geometry and connectedness of their subvarieties.

Findings

Ulrich bundles with $c_2(\\mathcal E)^2=0$ are classified on certain varieties.

Strong geometric constraints on the variety $X$ are established.

Disconnected Ulrich subvarieties are studied in detail.

Abstract

We give an almost complete classification of Ulrich bundles $\mathcal E$ with $c_2(\mathcal E)^2=0$ on a variety $X$ of dimension $n \ge 4$. Moreover, we show that there are strong constraints on the geometry of $X$ and we study disconnected Ulrich subvarieties.