Lines generate the Picard groups of certain fermat surfaces
Date
2015
Authors
Degtyarev, A.
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Source Title
Journal of Number Theory
Print ISSN
0022-314X
Electronic ISSN
1096-1658
Publisher
Elsevier
Volume
147
Issue
Pages
454 - 477
Language
English
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Abstract
We answer a question of T. Shioda and show that, for any positive integer m prime to 6, the Picard group of the Fermat surface Φm is generated by the classes of lines contained in Φm. A few other classes of surfaces are also considered. © 2014 Elsevier Inc.
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Keywords
Alexander module , Fermat surface , Néron-Severi group , Picard group , Primary , Secondary , 14J25 , 14J05 , 14H30