Generators of the Néron-Severi Group of a Fermat Surface

  • Noboru Aoki
  • Tetsuji Shioda
Part of the Progress in Mathematics book series (PM, volume 35)


The Néron-Severi group of a (nonsingular projective) variety is, by definition, the group of divisors modulo algebraic equivalence, which is known to be a finitely generated abelian group (cf. [2]). Its rank is called the Picard number of the variety. Thus the Néron-Severi group is defined in purely algebro-geometric terms, but it is a rather delicate invariant of arithmetic nature. Perhaps, because of this reason, it usually requires some nontrivial work before one can determine the Picard number of a given variety, let alone the full structure of its Néron-Severi group. This is the case even for algebraic surfaces over the field of complex numbers, where it can be regarded as the subgroup of the cohomology group H 2(X, ℤ) characterized by the Lefschetz criterion.


Fermat Surface Algebraic Cycle Picard Number Intersection Multiplicity Adjunction Formula 
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  1. [1]
    Aoki, N.: Properties of Dirichlet characters and its application to Fermat varieties. Master Thesis, University of Tokyo, 1982 (in Japanese).Google Scholar
  2. [2]
    Lang, S.: Diophantine geometry, Intersc. Publishers, New York-London, 1962.Google Scholar
  3. [3]
    Shioda, T.: The Hodge Conjecture for Fermat varieties, Math. Ann. 245 (1979), 175–184.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Shioda, T.: On the Picard number of a Fermat surface, J. Fac. Sci. Univ. Tokyo, Sec. IA, 28 (1982), 725–734.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Noboru Aoki
    • 1
  • Tetsuji Shioda
    • 1
  1. 1.Department of Mathematics Faculty of ScienceUniversity of TokyoHongo, Tokyo 113Japan

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