ACM bundles on cubic surfaces

Autores: Marta Casanellas Rius , Robin Hartshorne
Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 13, Nº 3, 2011, págs. 709-731
Idioma: inglés
DOI: 10.4171/jems/265
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Resumen
- In this paper we prove that, for every r = 2, the moduli space MsX (r; c1,c2) of rank r stable vector bundles with Chern classes c1 = rH and c2 = 1/2 (3r2 - 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.