On some “sporadic” moduli spaces of Ulrich bundles on some 3-fold scrolls over F0

We investigate the existence of some sporadic rank-r ⩾ 1 Ulrich vector bundles on suitable 3-fold scrolls X over the Hirzebruch surface F0, which arise as tautological embeddings of projectivization of very-ample vector bundles on F0 that are uniform in the sense of Brosius and Aprodu–Brinzanescu, cf. [11] and [4] respectively. Such Ulrich bundles arise as deformations of “iterative” extensions by means of sporadic Ulrich line bundles which have been contructed in our former paper [30] (where instead higher-rank sporadic bundles were not investigated therein). We explicitely describe irreducible components of the corresponding sporadic moduli spaces of rank r ⩾ 1 vector bundles which are Ulrich with respect to the tautological polarization on X. In some cases, such irreducible components turn out to be a singleton, in some other such components are generically smooth, whose positive dimension has been computed and whose general point turns out to be a slope-stable, indecomposable vector bundle.