Counting lines on surfaces

By Samuel Boissière, A. Sarti. 2006

60 citations recorded by the source corpus.

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. Cubic surface with 27 lines

Subfields: Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/91f0b5e42480952fd963efaabf5d6c16ebc4fe3f

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In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

Arrangements of curves and algebraic surfaces (2007, methodology): “The order we solve is the following: [[5, 6, 13]] solve for c7, [[3, 6, 15]] solve for b2, [[1, 9, 15]] solve for c8, [[5, 9, 12]] solve for c6, [[1, 10, 14]] solve for b3, [[3, 9, 11]] solve for b8, [[4, 8, 11]] solve for c3, [[4, 10, 13]] solve for c2, [[4, 7, 15]] solve for b1 and [[5, 7, 11]] so”
Lectures on K3 Surfaces (2016, background): “See [72, 498] for more details and a discussion of the possible configuration of these lines and Sections 3.”