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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)

Abstract

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.

Keywords

Fermat Surface Algebraic Cycle Picard Number Intersection Multiplicity Adjunction Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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