|
On Vorontsov's Theorem on K3 surfaces with non-symplectic group actions
Author(s):
Keiji
Oguiso;
De-Qi
Zhang
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1571-1580.
MSC (2000):
Primary 14J28
Posted:
February 25, 2000
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We shall give a proof for Vorontsov's Theorem and apply this to classify log Enriques surfaces with large prime canonical index.
References:
-
- [BPV]
- W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Springer-Verlag (1984). MR 86c:32026
- [Bl]
- R. Blache, The structure of l.c. surfaces of Kodaira dimension zero, I, J. Alg. Geom 4 (1995), 137 - 179. MR 95j:32042
- [Ka]
- Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603 - 633. MR 86c:14013b
- [Kd]
- K. Kodaira, On compact analytic surfaces
, Ann. of Math. 77 (1963), 563-626. MR 32:1730 - [Ko]
- S. Kondo, Automorphisms of algebraic
surfaces which act trivially on Picard groups, J. Math. Soc. Japan. 44 (1992), 75-98. MR 93e:14046 - [MM]
- M. Masley and L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286 (1976), 248-256. MR 55:2834
- [MO]
- N. Machida and K. Oguiso, On
surfaces admitting finite non-symplectic group actions, J. Math. Sci. Univ. Tokyo 5 (1998), no. 2, 273-297. CMP 98:16 - [Ne]
- A. Néron, Modéles minimaux des variétés abéliennes sur les corp locaux et globaux, Publ. Math. I.H.E.S. 21 (1964). MR 31:3423
- [Ni1]
- V. V. Nikulin, Finite groups of automorphisms of Kählerian surfaces of Type
, Moscow Math. Sod. 38 (1980), 71-137. MR 81e:32033 - [Ni2]
- V. V. Nikulin, Factor groups of the automorphism group of hyperbolic forms by the subgroups generated by
reflections, J. Soviet Math. 22 (1983), 1401-1475. - [Ni3]
- V. V. Nikulin, Integral symmetric bilinear forms and some of their applications, Izv. Math. 14 (1980), 103-167. MR 80j:10031
- [Og]
- K. Oguiso, On algebraic fiber space structures on a Calabi-Yau
-fold, Intern. J. Math. 4 (1993), 439-465. MR 94g:14019 - [OZ1]
- K. Oguiso and D.-Q. Zhang, On the most algebraic
surfaces and the most extremal log Enriques surfaces, Amer. J. Math. 118 (1996), 1277 - 1297. MR 97i:14022 - [OZ2]
- K. Oguiso and D.-Q. Zhang, On extremal log Enriques surfaces, II,, Tohoku Math. J. 50 (1998), 419 - 436. CMP 98:17
- [OZ3]
- K. Oguiso and D.-Q. Zhang, On the complete classification of extremal log Enriques surfaces, Math. Z. to appear.
- [PS-S]
- I. I. Piateckii-Shapiro, I. R. Shafarevich, A Torelli theorem for algebraic surfaces of type
, Math. USSR Izv. 5 (1971), 547-587. MR 44:1666 - [RS]
- A. N. Rudakov and I. R. Shafarevich, Surfaces of type
over fields of finite characteristic, Sovremennye Problemy Mathematiki 18 (1981), 115 - 207. MR 83c:14027 - [Sh]
- T. Shioda, On the Mordell-Weil lattices, Comment. Math. Univ. Sancti Pauli (1990), 211 - 240. MR 91m:14056
- [Ue]
- K. Ueno, A remark on automorphisms of Enriques surfaces, J. Fac. Sci. Univ. of Tokyo 23 (1976), 149 - 165. MR 53:8071
- [Vo]
- S. P. Vorontsov, Automorphisms of even lattices that arise in connection with automorphisms of algebraic
surfaces, Vestnik Mosk. Univ. Math. 38 (1983), 19-21. MR 84g:14038 - [Z1]
- D.-Q. Zhang, Logarithmic Enriques surfaces, I, J. Math. Kyoto Univ. 31 (1991), 419 - 466. MR 93d:14051
- [Z2]
- D.-Q. Zhang, Logarithmic Enriques surfaces, II, J. Math. Kyoto Univ. 33 (1993), 357 - 397. MR 95e:14028
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
14J28
Retrieve articles in all Journals with MSC
(2000):
14J28
Additional Information:
Keiji
Oguiso
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, Japan
Email:
oguiso@ms.u-tokyo.ac.jp
De-Qi
Zhang
Affiliation:
Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, Singapore 119260
Email:
matzdq@math.nus.edu.sg
DOI:
10.1090/S0002-9939-00-05427-7
PII:
S 0002-9939(00)05427-7
Received by editor(s):
April 11, 1997
Posted:
February 25, 2000
Communicated by:
Ron Donagi
Copyright of article:
Copyright
2000,
American Mathematical Society
|