Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the local algebraizability of real analytic generic submanifolds of
  C^n   We prove that the local (pseudo)group of biholomorphisms stabilizing a
minimal, finitely nondegenerate real algebraic submanifold in C^n is a real
algebraic local Lie group (the works of S.M. Baouendi, P. Ebenfelt, L.-P.
Rothschild and D. Zaitsev published in this direction restrict, without
understandable reason, to the isotropy group of a fixed central point). We
deduce necessary conditions for the local algebraizability of real analytic
rigid tubes of arbitrary codimension in C^n. Without using the Elie Cartan
equivalence algorithm, we explain the up to now only known example Im w =
e^(|z^2|), due to X. Huang, S. Ji and S.S. Yau in 2001, of a nonalgebraizable
Levi nondegenerate real analytic hypersurface of C^2. These elementary criteria
provide a first answer to an open problem raised by S.M. Baouendi, P. Ebenfelt
and L.-P. Rothschild, in the survey article : ``Local geometric properties of
real submanifolds in complex space'', Bull. Amer. Math. Soc. (N.S.) 37 (2000),
no. 3, 309--336. A second answer (necessary and sufficient condition) for local
algebraizability in the homogeneous case will appear subsequently.

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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph