TY - JOUR

T1 - Lines on Fermat surfaces

AU - Schütt, Matthias

AU - Shioda, Tetsuji

AU - van Luijk, Ronald

N1 - Funding information: Partial funding from DFG under grant Schu 2266/2-2 and JSPS under Grant-in-Aid for Scientific Research (C) No. 20540051 is gratefully acknowledged. * Corresponding author. E-mail addresses: schuett@math.uni-hannover.de (M. Schütt), shioda@rikkyo.ac.jp (T. Shioda), rvl@math.leidenuniv.nl (R. van Luijk). URLs: http://www.iag.uni-hannover.de/~schuett/ (M. Schütt), http://www.rkmath.rikkyo.ac.jp/math/shioda/ (T. Shioda), http://www.math.leidenuniv.nl/~rvl (R. van Luijk).

PY - 2010/9

Y1 - 2010/9

N2 - We prove that the Néron-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.

AB - We prove that the Néron-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.

KW - Fermat surface

KW - Néron-Severi group

KW - Primary

KW - Secondary

KW - Supersingular reduction

UR - http://www.scopus.com/inward/record.url?scp=77953692452&partnerID=8YFLogxK

UR - https://arxiv.org/abs/0812.2377

U2 - 10.1016/j.jnt.2010.01.008

DO - 10.1016/j.jnt.2010.01.008

M3 - Article

AN - SCOPUS:77953692452

VL - 130

SP - 1939

EP - 1963

JO - Journal of number theory

JF - Journal of number theory

SN - 0022-314X

IS - 9

ER -