# ACM bundles on cubic surfaces

### Marta Casanellas

Universitat Politecnica de Catalunya, Barcelona, Spain### Robin Hartshorne

University of California, Berkeley, USA

## Abstract

In this paper we prove that, for every *r* ≥ 2, the moduli space *MsX* (*r*; _c_1,_c_2) of rank *r* stable vector bundles with Chern classes _c_1 = *rH* and _c_2 = 1/2 (3_r_2 − *r*) on a nonsingular cubic surface *X* ⊂ ℙ3 contains a nonempty smooth open subset formed by ACM bundles, i.e. vector bundles with no intermediate cohomology. The bundles we consider for this study are extremal for the number of generators of the corresponding module (these are known as Ulrich bundles), so we also prove the existence of indecomposable Ulrich bundles of arbitrarily high rank on *X*.

## Cite this article

Marta Casanellas, Robin Hartshorne, ACM bundles on cubic surfaces. J. Eur. Math. Soc. 13 (2011), no. 3, pp. 709–731

DOI 10.4171/JEMS/265