Ulrich wildness of some decomposable threefold scrolls over ${\mathbb{F}}_a$

Abstract

The paper deals with Ulrich wildness of decomposable threefold scrolls $X$ over Hirzebruch surfaces ${\mathbb{F}}_a$, for any $a⩾0$. Our Main Theorem enstablishes that for $a=0$, the moduli space of rank-$r$ Ulrich bundles, for any $r⩾2$ and of given Chern classes, contains a generically smooth, unirational component $\mathcal{M}(r)$ of computed dimension whose general point corresponds to a slope-stable Ulrich bundle; in particular $X$ turns out to be Ulrich wild. When $a⩾1$ and in presence of modular obstructions, $X$ is nevertheless shown to be Ulrich wild too.

11 pages, submitted preprint