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      Lines generate the Picard groups of certain fermat surfaces

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      Author(s)
      Degtyarev, A.
      Date
      2015
      Source Title
      Journal of Number Theory
      Print ISSN
      0022-314X
      Electronic ISSN
      1096-1658
      Publisher
      Elsevier
      Volume
      147
      Pages
      454 - 477
      Language
      English
      Type
      Article
      Item Usage Stats
      123
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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.
      Keywords
      Alexander module
      Fermat surface
      Néron-Severi group
      Picard group
      Primary
      Secondary
      14J25
      14J05
      14H30
      Permalink
      http://hdl.handle.net/11693/22603
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jnt.2014.07.020
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      • Department of Mathematics 653
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