CR transversality of holomorphic mappings between generic submanifolds in complex spaces

Authors:
Peter Ebenfelt and Duong Ngoc Son

Journal:
Proc. Amer. Math. Soc. **140** (2012), 1729-1738

MSC (2010):
Primary 32H02, 32V20, 32V40

Published electronically:
September 9, 2011

MathSciNet review:
2869157

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a holomorphic mapping sending one generic submanifold into another of the same dimension is CR transversal to the target submanifold provided that the source manifold is of finite type and the map is of generic full rank. This result and its corollaries completely resolve two questions posed by Linda P. Rothschild and the first author in 2006. Another one of our main results, in the special setting of hypersurfaces, was also explicitly stated as a conjecture by B. Lamel and N. Mir in a paper from 2006.

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Additional Information

**Peter Ebenfelt**

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

Email:
pebenfel@math.ucsd.edu

**Duong Ngoc Son**

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

Email:
snduong@math.ucsd.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-11091-8

Received by editor(s):
September 25, 2010

Received by editor(s) in revised form:
January 25, 2011

Published electronically:
September 9, 2011

Additional Notes:
The first author was partly supported by NSF grant DMS-0701121.

The second author acknowledges a scholarship from the Vietnam Education Foundation for his graduate study at UC San Diego and a grant from NAFOSTED (Vietnam).

Communicated by:
Franc Forstneric

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.