Lines on Fermat surfaces

JOURNAL OF NUMBER THEORY

卷:130

Article

Schuett, Matthias¹  Shioda, Tetsuji^2,3  van Luijk, Ronald⁴ 

[1] Leibniz Univ Hannover, Inst Algebra Geometry, D-30167 Hannover, Germany

[2] Rikkyo Univ, Dept Math, Tokyo I718501, Japan

[3] Kyoto Univ, Rims, Kyoto 6068502, Japan

[4] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands

关键词: Fermat surface;    Neron-Severi group;    Supersingular reduction;   

DOI  :  10.1016/j.jnt.2010.01.008

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free