Lines on Fermat surfaces

Details Lines on Fermat surfaces Lines on Fermat surfaces

2008-12-12

arxiv.org/abs/0812.2377v3

Mathematics

Algebraic Geometry

29 pages; v3: major extension thanks to RvL who joined as third author; results and techniques strengthened, paper reorganised

Scientific paper

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.

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