Ulrich bundles on cubic fourfolds
Algebraic Geometry
2022-09-20 v3
Abstract
We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E appears as an extension of two Lehn-Lehn-Sorger-van Straten sheaves. Then we prove that a general deformation of E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.
Cite
@article{arxiv.2011.12622,
title = {Ulrich bundles on cubic fourfolds},
author = {Daniele Faenzi and Yeongrak Kim},
journal= {arXiv preprint arXiv:2011.12622},
year = {2022}
}
Comments
To appear in Comm. Math. Helv