Embeddings of a family of Danielewski hypersurfaces and certain \C^+-actions on \C^3

Abstract : We consider the family of complex polynomials in \C[x,y,z] of the form x^2y-z^2-xq(x,z). Two such polynomials P_1 and P_2 are equivalent if there is an automorphism \varphi of \C[x,y,z] such that \varphi(P_1)=P_2. We give a complete classification of the equivalence classes of these polynomials in the algebraic and analytic category.
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https://hal.archives-ouvertes.fr/hal-00499456
Contributor : Lucy Moser-Jauslin <>
Submitted on : Friday, July 9, 2010 - 3:41:20 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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Lucy Moser-Jauslin, Pierre-Marie Poloni. Embeddings of a family of Danielewski hypersurfaces and certain \C^+-actions on \C^3. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2006, 56 (5), pp.1567-1581. ⟨hal-00499456⟩

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