Dynamics of the Segre varieties of a real submanifold in complex space

Authors:
M. S. Baouendi, P. Ebenfelt and Linda Preiss Rothschild

Journal:
J. Algebraic Geom. **12** (2003), 81-106

DOI:
https://doi.org/10.1090/S1056-3911-02-00305-3

Published electronically:
July 17, 2002

MathSciNet review:
1948686

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Abstract | References | Additional Information

Abstract: For a smooth (or formal) generic submanifold of real codimension in complex space with , we introduce the notion of a formal Segre variety mapping and its iterated Segre mappings at , , . The Segre variety mapping extends the notion of Segre varieties of a real-analytic generic submanifold to the setting of smooth (or formal) submanifolds. One of the main results in this paper is that is of finite type (in the sense of Kohn and Bloom-Graham) at if and only if there exists such that the (generic) rank of is . More generally, we prove that parameterizes the local CR orbit of at .

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Additional Information

**M. S. Baouendi**

Affiliation:
Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112

Email:
sbaouendi@ucsd.edu

**P. Ebenfelt**

Affiliation:
Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112

Email:
pebenfel@ucsd.edu

**Linda Preiss Rothschild**

Affiliation:
Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112

Email:
lrothschild@ucsd.edu

DOI:
https://doi.org/10.1090/S1056-3911-02-00305-3

Received by editor(s):
August 16, 2000

Published electronically:
July 17, 2002

Additional Notes:
The first and the third authors are partially supported by National Science Foundation grant DMS 98-01258. The second author is partially supported by a grant from the Swedish Natural Science Research Council.