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Deformation of generic submanifolds in a complex manifold

M. S. Baouendi·L. P. Rothschild·D. Zaitsev
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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.

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M. S. Baouendi, L. P. Rothschild, D. Zaitsev. 2006-08-12. Deformation of generic submanifolds in a complex manifold. https://arxiv.org/abs/math/0608296

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