ACM bundles on cubic surfaces
Marta Casanellas
Universitat Politecnica de Catalunya, Barcelona, SpainRobin Hartshorne
University of California, Berkeley, USA
Abstract
In this paper we prove that, for every , the moduli space of rank stable vector bundles with Chern classes and on a nonsingular cubic surface 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 .
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