Deformation of generic submanifolds in a complex manifold

• Autores: M. Salah Baouendi, L.P. Rothschild, D. Zaitsev
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 1, 2007, págs. 157-180
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.01.019
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• Resumen

  • 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 Thom's transversality theorem, as well as the stratification of real-algebraic sets. Optimal results on the order of nondegeneracy are given.