|
Automorphism groups on normal singular cubic surfaces with no parameters
Author(s):
Yoshiyuki
Sakamaki
Journal:
Trans. Amer. Math. Soc.
362
(2010),
2641-2666.
MSC (2010):
Primary 14J50;
Secondary 14J17
Posted:
December 3, 2009
MathSciNet review:
2584614
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The classification of normal singular cubic surfaces in  over a complex number field  was given by J. W. Bruce and C. T. C. Wall. In this paper, first we prove their results by a different way, second we provide normal forms of normal singular cubic surfaces according to the type of singularities, and finally we determine automorphism groups on normal singular cubic surfaces with no parameters.
References:
-
- 1.
- A. Beauville, Complex Algebraic Surfaces. London Mathematical Society Lecture Note Series 68. Cambridge Univ. Press, 1983. MR 732439 (85a:14024)
- 2.
- J. W. Bruce and C. T. C. Wall, On the classification of cubic surfaces. J. London Math. Soc. (2) 19 (1979), no. 2, 245-256. MR 533323 (80f:14021)
- 3.
- A. Cayley, A memoir on cubic surfaces. Phil. Trans. Roy. Soc., 159 (1869), 231-326.
- 4.
- D. F. Coray and M. A. Tsfasman, Arithmetic on singular Del Pezzo surfaces. Proc. London Math. Soc. (3) 57 (1988), no. 1, 25-87. MR 940430 (89f:11083)
- 5.
- M. Demazure, Surfaces de del Pezzo II-V. Séminaire sur les Singularités des Surfaces, Lecture Notes in Math., Vol. 777, Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 579026 (82d:14021)
- 6.
- I. V. Dolgachev and V. A. Iskovskikh, Finite subgroups of the plane Cremona group. arXiv:math/0610595v2 [math.AG] 21 Jul 2007.
- 7.
- J. Harris, Algebraic geometry. Graduate Texts in Mathematics, 133, Springer-Verlag, New York, 1995. MR 1416564 (97e:14001)
- 8.
- R. Hartshorne, Algebraic Geometry. Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977. MR 0463157 (57:3116)
- 9.
- T. Hosoh, Automorphism groups of cubic surfaces. J. Algebra 192 (1997), no. 2, 651-677. MR 1452681 (99d:14042)
- 10.
- T. Hosoh, Automorphism groups of quartic del Pezzo surfaces. J. Algebra 185 (1996), no. 2, 374-389. MR 1417377 (97i:14026)
- 11.
- S. Iitaka, Algebraic Geometry. Graduate Texts in Mathematics, 76. Springer-Verlag, New York-Berlin, 1982. MR 637060 (84j:14001)
- 12.
- Y. Kawamata, Algebraic Varieties. Kyoritsu Shuppan Co., Ltd., 1997.
- 13.
- M. Koitabashi, Automorphism groups of generic rational surfaces. J. Algebra 116 (1988), no. 1, 130-142.
MR 944150 (89f:14045) - 14.
- M. Reid, Young person's guide to canonical singularities. Proc. Sympos. Pure Math, 46-1(1987), 345-414. MR 927963 (89b:14016)
- 15.
- Y. Manin, Cubic Forms: Algebra, Geometry, Arithmetic. North-Holland, Amsterdam, 1974.
MR 833513 (87d:11037) - 16.
- L. Schläfli, On the distribution of surfaces of the third order into species. Phil. Trans. Roy. Soc., 153 (1864), 193-247.
- 17.
- B. Segre, The Non-singular Cubic Surfaces. Oxford University Press, Oxford, 1942. MR 0008171 (4:254b)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2010):
14J50,
14J17
Retrieve articles in all Journals with
MSC (2010):
14J50,
14J17
Additional Information:
Yoshiyuki
Sakamaki
Affiliation:
Graduate School of Mathematics, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka, 812-8581, Japan
Address at time of publication:
System Engineering Laboratory, Toshiba Corporate Research & Development Center, 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi, Kanagawa, 212-8582, Japan
Email:
sakamaki@math.kyushu-u.ac.jp, yoshiyuki.sakamaki@toshiba.co.jp
DOI:
10.1090/S0002-9947-09-05023-5
PII:
S 0002-9947(09)05023-5
Keywords:
Algebraic geometry,
automorphism groups,
cubic surfaces,
singularities,
blowing-up,
infinitely near points
Received by editor(s):
November 13, 2007
Received by editor(s) in revised form:
July 29, 2008
Posted:
December 3, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
