|
Which singular K3 surfaces cover an Enriques surface
Author(s):
Ali
Sinan
Sertöz
Journal:
Proc. Amer. Math. Soc.
133
(2005),
43-50.
MSC (2000):
Primary 14J28;
Secondary 11E39
Posted:
August 20, 2004
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- 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
-Sapiro, I. I.; Safarevic, I. R., Torelli's theorem for algebraic surfaces of type . (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 35, (1971), 530-572. MR 0284440 (44:1666) - 14.
- Shioda, T.; Inose, H. On singular
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)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
14J28,
11E39
Retrieve articles in all Journals with MSC
(2000):
14J28,
11E39
Additional Information:
Ali
Sinan
Sertöz
Affiliation:
Department of Mathematics, Bilkent University, TR-06800 Ankara, Turkey
Email:
sertoz@bilkent.edu.tr
DOI:
10.1090/S0002-9939-04-07666-X
PII:
S 0002-9939(04)07666-X
Keywords:
K3 surfaces,
Enriques surfaces,
integral lattices
Received by editor(s):
February 15, 2003
Received by editor(s) in revised form:
October 9, 2003
Posted:
August 20, 2004
Additional Notes:
This research was partially supported by TÜBITAK-BDP
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|