Geodesic
ACM bundles on cubic surfaces
Journal of the European Mathematical Society, Tome 13 (2011) no. 3, pp. 709-731

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In this paper we prove that, for every r≥2, the moduli space MXs​(r;c1​,c2​) of rank r stable vector bundles with Chern classes c1​=rH and c2​=21​(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.
DOI : 10.4171/jems/265
Classification : 14-XX, 13-XX, 00-XX
Keywords: ACM vector bundles, Cohen-Macaulay modules, Ulrich bundles, moduli space of vector bundles, cubic surface 
Marta Casanellas; Robin Hartshorne. ACM bundles on cubic surfaces. Journal of the European Mathematical Society, Tome 13 (2011) no. 3, pp. 709-731. doi: 10.4171/jems/265
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     title = {ACM bundles on cubic surfaces},
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     year = {2011},
     volume = {13},
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     doi = {10.4171/jems/265},
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