# Ulrich and aCM bundles from invariant theory

## TL;DR

This paper constructs special arithmetically Cohen-Macaulay (aCM) and Ulrich vector bundles on hypersurfaces using invariant theory, revealing new bundles on general cubic hypersurfaces and fourfolds.

## Contribution

It introduces a method using prehomogeneous representations to construct aCM and Ulrich bundles on hypersurfaces, including new examples on cubic fourfolds and sevenfolds.

## Key findings

- A general cubic hypersurface of dimension seven admits an indecomposable Ulrich bundle of rank nine.
- A general cubic fourfold admits an unsplit aCM bundle of rank six.
- The method links invariant theory with vector bundle construction on hypersurfaces.

## 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 admitsan indecomposable Ulrich bundle of rank nine, and that a general cubic fourfold admits an unsplit aCM bundle of rank six.