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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9939-2011-11091-8
PII: S 0002-9939(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.