Vector bundles whose restriction to a linear section is Ulrich

TL;DR

The paper introduces delta-Ulrich sheaves on ACM varieties, constructed via representation theory, which restrict to Ulrich sheaves on general linear sections, and demonstrates their existence in certain embeddings.

Contribution

It proves the existence of delta-Ulrich sheaves on all normal ACM varieties using representation theory, linking them to semistable instanton bundles in the surface case.

Findings

Existence of delta-Ulrich sheaves on all normal ACM varieties.

Construction of delta-Ulrich sheaves via Roby-Clifford algebra representations.

High Veronese embeddings admit delta-Ulrich sheaves with global sections.

Abstract

An Ulrich sheaf on an n-dimensional projective variety X, embedded in a projective space, is a normalized 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 delta-Ulrich. In the case n=2, where delta-Ulrich sheaves satisfy the property that their direct image under a general finite linear projection is a semistable instanton bundle, we show that some high Veronese embedding of X admits a delta-Ulrich sheaf with a global section.