Ulrich and aCM bundles from invariant theory

Abstract

We use certain special prehomogeneous representations of algebraic groups in order to construct aCM vector bundles, possibly Ulrich, on certain families of hypersurfaces. Among other results, we show that a general cubic hypersurface of dimension seven admits an indecomposable Ulrich bundle of rank nine, and that a general quartic fourfold admits an unsplit aCM bundle of rank six.

Keywords:

• aCM bundle
• hypersurface
• invariant theory
• prehomogeneous space
• Ulrich bundle

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 14F05
• 14J7
• 20G05
• 20G41

Acknowledgements

We would like to thank Roland Abuaf, Marcello Bernardara, Daniele Faenzi, Sasha Kuznetsov, Rosa Miró-Roig and Joan Pons-Llopis for useful discussions.