Lines on Fermat surfaces
By M. Schuett, T. Shioda, Ronald van Luijk. 2008
47 citations recorded by the source corpus.
We prove that the Neron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relatively prime to 6. The proof uses reduction modulo a supersingular prime. The techniques are developed in detail. They can be applied to other surfaces and varieties as well.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/95c36c0505aecec43d740871af895ca7a09c68bb
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- 64 lines on smooth quartic surfaces (2012, background): “ fact, this is a supersingular K3 surface of Artin invariant one which has continued to attract mathematicians’ attention, starting from Shioda [18] and Mizukami [10] all the way to the recent papers [15] and [6]. We conjecture that 112 is the maximum number of lines on a smooth quartic surface in c”