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Which singular K3 surfaces cover an Enriques surface

Author: Ali Sinan Sertöz
Journal: Proc. Amer. Math. Soc. 133 (2005), 43-50
MSC (2000): Primary 14J28; Secondary 11E39
Published electronically: August 20, 2004
MathSciNet review: 2085151
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Abstract: We determine the necessary and sufficient conditions on the entries of the intersection matrix of the transcendental lattice of a singular K3 surface for the surface to doubly cover an Enriques surface.

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  • 1. Barth, W., Peters, C. and Van de Ven, A., Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, 1984. MR 0749574 (86c:32026)
  • 2. Benedetti, R. and Petronio, C., Lectures on Hyperbolic Geometry, Springer-Verlag, Universitext, 1992. MR 1219310 (94e:57015)
  • 3. Birkhoff, G. and Mac Lane, S., A Survey of Modern Algebra, MacMillan, 1941. MR 0005093 (3:99h)
  • 4. Degtyarev, A., Itenberg, I. and Kharlamov, V., Real Enriques Surfaces, Lecture Notes in Mathematics Vol. 1746, Springer-Verlag, 2000. MR 1795406 (2001k:14100)
  • 5. Horikawa, E., On the periods of Enriques surfaces-I, Math. Ann. 234 (1978), 73-88. MR 0491725 (58:10927a)
  • 6. Horikawa, E., On the periods of Enriques surfaces-II, Math. Ann. 235 (1978), 217-246. MR 0491725 (58:10927b)
  • 7. Keum, J. H., Every algebraic Kummer surface is the K3-cover of an Enriques surface, Nagoya Math. J., 118 (1990), 99-110. MR 1060704 (91f:14036)
  • 8. Morrison, D. R., On K3 surfaces with large Picard number, Invent. Math., 75 (1984), 105-121. MR 0728142 (85j:14071)
  • 9. Milnor, J. and Husemoller, D., Symmetric Bilinear Forms, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, 1973. MR 0506372 (58:22129)
  • 10. Nikulin, V., On Kummer surfaces, Math. USSR Isvestija, 9 (1975), 261-275. MR 0429917 (55:2926)
  • 11. Nikulin, V., Integral quadratic bilinear forms and some of their applications, Math. USSR Isvestija, 14 (1980), 103-167. MR 0525944 (80j:10031)
  • 12. Niven, I., Zuckerman, H.S. and Montgomery, H.L., An Introduction to the Theory of Numbers, John Wiley and Sons, 1991. MR 1083765 (91i:11001)
  • 13. Pjatecki{\u{\i}}\kern.15em-Sapiro, I. I.; Safarevic, I. R., Torelli's theorem for algebraic surfaces of type ${\rm K}3$. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 35, (1971), 530-572. MR 0284440 (44:1666)
  • 14. Shioda, T.; Inose, H. On singular $K3$surfaces. Complex analysis and algebraic geometry, pp. 119-136. Iwanami Shoten, Tokyo, 1977. MR 0441982 (56:371)
  • 15. Vinberg, E. B., On groups of unit elements of certain quadratic forms, Math. USSR Sbornik, 16 (1972), 17-35. MR 0295193 (45:4261)

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Additional Information

Ali Sinan Sertöz
Affiliation: Department of Mathematics, Bilkent University, TR-06800 Ankara, Turkey

Keywords: K3 surfaces, Enriques surfaces, integral lattices
Received by editor(s): February 15, 2003
Received by editor(s) in revised form: October 9, 2003
Published electronically: August 20, 2004
Additional Notes: This research was partially supported by TÜBİTAK-BDP
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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