Ulrich bundles on cubic fourfolds

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.

To appear in Comm. Math. Helv

References in corpus (2)

• Stability conditions in families
• An explicit matrix factorization of cubic hypersurfaces of small dimension

Cited by in corpus (1)

• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds