Vector bundles whose restriction to a linear section is Ulrich
An Ulrich sheaf on an n-dimensional projective variety X ⊆ P^ NX⊆ PN 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 δ-Ulrich. In the case n= 2, n= 2,
where δ δ-Ulrich sheaves satisfy the property that their direct image under a general finite�…
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 δ-Ulrich. In the case n= 2, n= 2,
where δ δ-Ulrich sheaves satisfy the property that their direct image under a general finite�…
Abstract
An Ulrich sheaf on an n-dimensional projective variety 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 -Ulrich. In the case where -Ulrich sheaves satisfy the property that their direct image under a general finite linear projection to is a semistable instanton bundle on , we show that some high Veronese embedding of X admits a -Ulrich sheaf with a global section.
Springer