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Fano surfaces with 12 or 30 elliptic curves. (English) Zbl 1225.14029
The author studies the properties of Fano surfaces with a fixed number of elliptic curves. We recall that a Fano surface is a surface of general type parametrizing the lines of a smooth cubic threefold.
The paper gives an application of the results of a previous work [Manuscr. Math. 129, No. 3, 381–399 (2009; Zbl 1177.14079)], to the case of surfaces having 12 or 30 elliptic curves, describing the first ones as ramified triple covers of an abelian surface and computing their Néron-Severi group. In the latter case, the author focuses on the Fermat cubic, explicitly computing the configuration of the 30 elliptic curves and the generators of the Néron-Severi group.

14J29 Surfaces of general type
14J50 Automorphisms of surfaces and higher-dimensional varieties
14C20 Divisors, linear systems, invertible sheaves
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