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Lines on Fermat surfaces |
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| Authors: | Matthias Schütt Tetsuji Shioda Ronald van Luijk |
| Institution: | a Institute for Algebraic Geometry, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany b Department of Mathematics, Rikkyo University, Tokyo 171-8501, Japan c RIMS, Kyoto University, Kyoto 606-8502, Japan d Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden, The Netherlands |
| Abstract: | 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. |
| Keywords: | primary 14J25 secondary 11G25 14C22 |
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