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Smooth Kummer surfaces
in projective three-space

Author: Thomas Bauer
Journal: Proc. Amer. Math. Soc. 125 (1997), 2537-2541
MSC (1991): Primary 14J28; Secondary 14E25
MathSciNet review: 1422846
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Abstract: In this note we prove the existence of smooth Kummer surfaces in projective three-space containing sixteen mutually disjoint smooth rational curves of any given degree.

References [Enhancements On Off] (What's this?)

  • 1. W. Barth and Th. Bauer, Smooth quartic surfaces with 352 conics, Manuscripta Math. 85 (1994), no. 3-4, 409–417. MR 1305751, 10.1007/BF02568207
  • 2. W. Barth and I. Nieto, Abelian surfaces of type (1,3) and quartic surfaces with 16 skew lines, J. Algebraic Geom. 3 (1994), no. 2, 173–222. MR 1257320
  • 3. Th. Bauer, Projective images of Kummer surfaces, Math. Ann. 299 (1994), no. 1, 155–170. MR 1273081, 10.1007/BF01459777
  • 4. Lucien Godeaux, Sur la surface du quatrième ordre contenant trente-deux droites, Acad. Roy. Belgique. Bull. Cl. Sci. (5) 25 (1939), 539–552 (French). MR 0008165
  • 5. Isao Naruki, On smooth quartic embedding of Kummer surfaces, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), no. 7, 223–225. MR 1137912
  • 6. Nikulin, V.V.: On Kummer surfaces. Math. USSR Izvestija, Vol.9, No.2, 261-275 (1975)
  • 7. B. Saint-Donat, Projective models of 𝐾-3 surfaces, Amer. J. Math. 96 (1974), 602–639. MR 0364263
  • 8. Traynard, E.: Sur les fonctions thêta de deux variables et les surfaces hyperelliptiques. Ann. Scient. Éc. Norm. Sup., 3. sér., t. 24, 77-177 (1907)

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Additional Information

Thomas Bauer
Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1$\tfrac12$, D-91054 Erlangen, Germany
Address at time of publication: Department of Mathematics, University of California, Los Angeles, California 90024

Received by editor(s): April 6, 1996
Additional Notes: The author was supported by DFG contract Ba 423/7-1.
Communicated by: Ron Donagi
Article copyright: © Copyright 1997 American Mathematical Society