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Automorphism groups on normal singular cubic surfaces with no parameters


Author: Yoshiyuki Sakamaki
Journal: Trans. Amer. Math. Soc. 362 (2010), 2641-2666
MSC (2010): Primary 14J50; Secondary 14J17
Published electronically: December 3, 2009
MathSciNet review: 2584614
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Abstract: The classification of normal singular cubic surfaces in $ \mathbf{P}^3$ over a complex number field $ \mathbf{C}$ 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.


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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: http://dx.doi.org/10.1090/S0002-9947-09-05023-5
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
Published electronically: December 3, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.