Reflection ideals and mappings between generic submanifolds in complex space

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dc.creatorBaouendi, M. S.
dc.creatorMir, Nordine
dc.creatorRothschild, Linda Preiss
dc.date2000-12-23
dc.date.accessioned2026-07-07T04:39:24Z
dc.date.available2026-07-07T04:39:24Z
dc.descriptionIn this paper, we study formal mappings between smooth generic submanifolds in multidimensional complex space and establish results on finite determination, convergence and local biholomorphic and algebraic equivalence. Our finite determination result gives sufficient conditions to guarantee that a formal map as above is uniquely determined by its jet at a point of a preassigned order. For real-analytic generic submanifolds, we prove convergence of formal mappings under appropriate assumptions and also give natural geometric conditions to assure that if two germs of such submanifolds are formally equivalent, then they are necessarily biholomorphically equivalent. If the submanifolds are moreover real-algebraic, we address the question of deciding when biholomorphic equivalence implies algebraic equivalence. In particular, we prove that if two real-algebraic hypersurfaces in $\C^N$ are biholomorphically equivalent, then they are in fact algebraically equivalent. All the results are first proved in the more general context of ``reflection ideals" associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds.
dc.description36 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0012243
dc.identifierhttp://arxiv.org/abs/math/0012243
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60647
dc.subjectComplex Variables
dc.subject32H02
dc.titleReflection ideals and mappings between generic submanifolds in complex space
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