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

Lucy Moser-Jauslin (1) , Pierre-Marie Poloni (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: equivalence of polynomials; stable equivalence; algebraic embeddings; Danielewski surfaces

Domaines: Géométrie algébrique [math.AG]

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, 2006, 56 (5), pp.1567-1581. ⟨hal-00499456⟩