Deformation of generic submanifolds in a complex manifold
Complex Variables
2007-05-23 v1 Differential Geometry
Abstract
This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces of embeddings satisfying certain nondegeneracy properties, and also make use of the Thom transversality theorem, as well as the stratification of real-algebraic sets. Optimal results on the order of nondegeneracy are given.
Keywords
Cite
@article{arxiv.math/0608296,
title = {Deformation of generic submanifolds in a complex manifold},
author = {M. S. Baouendi and L. P. Rothschild and D. Zaitsev},
journal= {arXiv preprint arXiv:math/0608296},
year = {2007}
}
Comments
24 pages