Abstract
The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That means that we give the number of such curves, their intersections and a plane model. This classification is linked to the classification of the automorphism groups of theses surfaces.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Roulleau, X. Elliptic curve configurations on Fano surfaces. manuscripta math. 129, 381–399 (2009). https://doi.org/10.1007/s00229-009-0264-5
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DOI: https://doi.org/10.1007/s00229-009-0264-5