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

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.