Deformation of generic submanifolds in a complex manifold
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Citation:M.S. Baouendi, L.P. Rothschild and D. Zaitsev 'Deformation of generic submanifolds in a complex manifold' in Advances in Mathematics, 212, (1), 2007, pp 157-180
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.
Science Foundation Ireland
Keywords:Pure & Applied Mathematics
Series/Report no:Advances in Mathematics