64 lines on smooth quartic surfaces
By S. Rams, M. Schuett. 2012
59 citations recorded by the source corpus.
Let $$k$$k be a field of characteristic $$p\ge 0$$p≥0 with $$p\ne 2,3$$p≠2,3. We prove that there are no geometrically smooth quartic surfaces $$S \subset \mathbb {P}^3_k$$S⊂Pk3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on $$S$$S.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/183c7e8922e2bbe52fd9af72ba6122c454a3b1fb
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- D. Huybrechts
- E. Markman
- Kieran G. O’Grady
- P. Stellari
- Emanuele Macrì
- Keiji Oguiso
- Ulrike Riess
- Justin Sawon
Citations in the corpus
- 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.”