Special Ulrich bundles on non-special surfaces with pg = q = 0

Abstract

Let [Formula: see text] be a surface with [Formula: see text] and endowed with a very ample line bundle [Formula: see text] such that [Formula: see text]. We show that [Formula: see text] supports special (often stable) Ulrich bundles of rank [Formula: see text], extending a recent result by A. Beauville. Moreover, we show that such an [Formula: see text] supports families of dimension [Formula: see text] of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large [Formula: see text] except for very few cases. We also show that the same is true for each linearly normal non-special surface with [Formula: see text] in [Formula: see text] of degree at least [Formula: see text], Enriques surface and anticanonical rational surface.