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Counting lines on surfaces

Samuel Boissière, Alessandra Sarti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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 a symmetric octic with 352 lines, and give examples of surfaces of degree d containing a sequence of d ( d - 2 ) + 4 skew lines.

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