Ulrich and aCM bundles from invariant theory

Laurent Manivel (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 cubic fourfold admits an unsplit aCM bundle of rank six.

Mots clés: Ulrich bundle; ACM bundle; hypersurface; prehomogeneous

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Laurent Manivel. Ulrich and aCM bundles from invariant theory. Communications in Algebra, 2019, 47 (2), pp.706-718. ⟨hal-01739650⟩