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Every algebraic Kummer surface is the K3-cover of an Enriques surface

  • Jong Hae Keum (a1)
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A Kummer surface is the minimal desingularization of the surface T/i, where T is a complex torus of dimension 2 and i the involution automorphism on T. T is an abelian surface if and only if its associated Kummer surface is algebraic. Kummer surfaces are among classical examples of K3-surfaces (which are simply-connected smooth surfaces with a nowhere-vanishing holomorphic 2-form), and play a crucial role in the theory of K3-surfaces. In a sense, all Kummer surfaces (resp. algebraic Kummer surfaces) form a 4 (resp. 3)-dimensional subset in the 20 (resp. 19)-dimensional family of K3-surfaces (resp. algebraic K3 surfaces).

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References
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[Bour] Bourbaki, N., Groupes et Algebres de Lie, Chap. IV, V, VI., Paris, Hermann, 1968.
[B-P-V] Barth, W., Peters, C., Van de Ven, A., Compact Complex Surfaces, Springer-Verlag, Berlin-Heidelberg, 1984.
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[S-M] Shioda, T., Mitani, N., Singular abelian surfaces and binary quadratic forms, in “Classification of algebraic varieties and compact complex manifolds”, Spr. Lee. Notes, No. 412, 1974.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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