Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A hypersurface in $\mathbb{C}^2$ whose stability group is not determined by $2$-jets

Author(s): R. Travis Kowalski
Journal: Proc. Amer. Math. Soc. 130 (2002), 3679-3686.
MSC (2000): Primary 32H12, 32V20
Posted: May 15, 2002
MathSciNet review: 1920048
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We give an example of a hypersurface in $\mathbb{C}^2$ through $0$ whose stability group at $0$ is determined by $3$-jets, but not by jets of any lesser order. We also examine some of the properties which the stability group of this infinite type hypersurface shares with the $3$-sphere in $\mathbb{C}^2$.


References:

[BER00]
M. S. Baouendi, P. Ebenfelt, and L. P. Rothschild, Local geometric properties of real submanifolds in complex space, Bull. Amer. Math. Soc. (N.S.) 37 (2000) no. 3, 309-336 (electronic). MR 2001a:32043

[BG77]
T. Bloom and I. Graham, On ``type'' conditions for generic real submanifolds of $\mathbb{C}^n$, Invent. Math. 40 (1977) no. 3, 217-243. MR 58:28644

[CM74]
S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. MR 54:13112

[ELZ00]
P. Ebenfelt, B. Lamel, and D. Zaitsev, Finite jet determination of local analytic CR automorphisms and their parametrization by $2$-jets in the finite type case, E-print: http://arXiv.org/abs/math.CV/0107013, (2000).

[Koh72]
J. J. Kohn, Boundary behavior of $\bar{\partial}$ on weakly pseudo-convex manifolds of dimension two, J. Differential Geometry 6 (1972), 523-542. MR 48:727

[Kow01]
R. T. Kowalski, Rational jet dependence of formal equivalences between real-analytic hypersurfaces in $\mathbb{C}^2$, E-print: http://arXiv.org/abs/math.CV/0108165, (2001).

[Poi07]
H. Poincaré, Les fonctions analytiques de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo, II. Ser. 23 (1907), 544-547.

[Vit90]
A. G. Vitushkin, Several complex variables. I (Translation by P. M. Gauthier), Springer-Verlag, Berlin, 1990, pp. 159-214. MR 90j:32003


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32H12, 32V20

Retrieve articles in all Journals with MSC (2000): 32H12, 32V20


Additional Information:

R. Travis Kowalski
Affiliation: Department of Mathematics, 0112, University of California, San Diego, La Jolla, California 92093-0112
Email: kowalski@math.ucsd.edu

DOI: 10.1090/S0002-9939-02-06545-0
PII: S 0002-9939(02)06545-0
Received by editor(s): July 31, 2001
Posted: May 15, 2002
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2002, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia