M. Casanellas: ACM bundles on cubic surfaces.

Abstract. In a joint work with R.Hartshorne we prove that, for every r≥2, the moduli space M^s_X(r;c₁,c₂) of rank r stable vector bundles with Chern classes c₁=rH and c2=(3r²-r)/2 on a nonsingular cubic surface X contained in 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. In this talk we will motivate the problem an we will relate it to liaison theory on the cubic surface.