Vector bundles whose restriction to a linear section is Ulrich

An Ulrich sheaf on an n -dimensional projective variety X ⊆ P N is an initialized ACM sheaf which has the maximum possible number of global sections. Using a construction based on the representation theory of Roby–Clifford algebras, we prove that every normal ACM variety admits a reflexive sheaf whose restriction to a general 1-dimensional linear section is Ulrich; we call such sheaves δ -Ulrich. In the case n = 2 , where δ -Ulrich sheaves satisfy the property that their direct image under a general finite linear projection to P 2 is a semistable instanton bundle on P 2 , we show that some high Veronese embedding of X admits a δ -Ulrich sheaf with a global section.