Fano surfaces with 12 or 30 elliptic curves

Details Fano surfaces with 12 or 30 elliptic curves Fano surfaces with 12 or 30 elliptic curves

2010-01-27

arxiv.org/abs/1001.4855v2

Mathematics

Algebraic Geometry

17 pages, minor changes, to be published in Michigan Math. J

Scientific paper

Curves of low genus on a surface carry important informations on that
surface. We study the Fano surfaces of lines of cubic threefolds that contain
12 or 30 elliptic curves. We determine their Picard number and compute a basis
of the N\'eron-Severi group of the Fano surface of the Fermat cubic threefold.

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