English

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.

Keywords

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

R2 v1 2026-06-23T20:29:52.494Z