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Smooth Kummer surfaces in projective three-space
Author(s):
Thomas
Bauer
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2537-2541.
MSC (1991):
Primary 14J28;
Secondary 14E25
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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:
- 1.
- Barth, W., Bauer, Th.: Smooth quartic surfaces with 352 conics. Manuscripta Math. 85, 409-417 (1994) MR 95j:14045
- 2.
- Barth, W., Nieto, I.: Abelian surfaces of type
 and quartic surfaces with 16 skew lines. J. Algebraic Geometry 3, 173-222 (1994)MR 95e:14033 - 3.
- Bauer, Th.: Projective images of Kummer surfaces. Math. Ann. 299, 155-170 (1994) MR 95c:14040
- 4.
- Godeaux, L.: Sur la surface du quatrième ordre contenant trente-deux droites. Académie Royale de Belgique, Bulletin de la Classe des Sciences, 5. sér., 25, 539-552 (1939) MR 4:253e
- 5.
- Naruki, I.: On smooth quartic embedding of Kummer surfaces. Proc. Japan Acad. 67, Ser. A, 223-225 (1991) MR 93b:14064
- 6.
- Nikulin, V.V.: On Kummer surfaces. Math. USSR Izvestija, Vol.9, No.2, 261-275 (1975)
- 7.
- Saint-Donat, B.: Projective models of K3 surfaces. Amer. J. Math. 96, 602-639 (1974) MR 51:518
- 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$\tfrac 12$, D-91054 Erlangen, Germany
Address at time of publication:
Department of Mathematics, University of California, Los Angeles, California 90024
Email:
bauerth@mi.uni-erlangen.de, tbauer@math.ucla.edu
DOI:
10.1090/S0002-9939-97-04089-6
PII:
S 0002-9939(97)04089-6
Received by editor(s):
April 6, 1996
Additional Notes:
The author was supported by DFG contract Ba 423/7-1.
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1997,
American Mathematical Society
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