Lines on Fermat surfaces
Algebraic Geometry
2009-09-30 v3 Number Theory
Abstract
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.
Cite
@article{arxiv.0812.2377,
title = {Lines on Fermat surfaces},
author = {Matthias Schuett and Tetsuji Shioda and Ronald van Luijk},
journal= {arXiv preprint arXiv:0812.2377},
year = {2009}
}
Comments
29 pages; v3: major extension thanks to RvL who joined as third author; results and techniques strengthened, paper reorganised