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Counting lines on surfaces

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arxiv math/0606100 v1 pith:7RFWZ5TN submitted 2006-06-05 math.AG

Samuel Boissiere , Alessandra Sarti This is my paper · ORCID
classification math.AG
keywords linessurfacesnumberclassicalconstructionscontainscountingcubic
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This paper deals with surfaces with many lines. It is well-known that a cubic contains 27 of them and that the maximal number for a quartic is 64. In higher degree the question remains open. Here we study classical and new constructions of surfaces with high number of lines. We obtain in particular a symmetric octic with 352 lines.

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  1. Anomaly cancellation for two $U(1)$ factors

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    Abelian anomaly cancellation for rank-K U(1) summands equates to finding (K-1)-planes on a cubic hypersurface over Q; for K=2 and six fermions this is the Fano surface of the Segre cubic, whose rational components ful...

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