Lines generate the Picard groups of certain fermat surfaces
Author(s)
Date
2015Source Title
Journal of Number Theory
Print ISSN
0022-314X
Electronic ISSN
1096-1658
Publisher
Elsevier
Volume
147
Pages
454 - 477
Language
English
Type
ArticleItem Usage Stats
123
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views
123
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downloads
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.
Keywords
Alexander moduleFermat surface
Néron-Severi group
Picard group
Primary
Secondary
14J25
14J05
14H30