Classification of degree 2 polynomial automorphisms of C3

• Autores: John Erik Fornaess, He Wu
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 1, 1998, págs. 195-210
• Idioma: inglés
• Títulos paralelos:
  • Clasificación de automorfismos polinomiales de 2 grados de C3
• Enlaces
  • Texto completo
• Resumen

  • For the family of degree at most $2$ polynomial self-maps of $\Bbb C^3$ with nowhere vanishing Jacobian determinant, we give the following classification: for any such map $f$, it is affinely conjugate to one of the following maps:

    (i) An affine automorphism;

    (ii) An elementary polynomial autormorphism $$ E(x,y,z)=(P(y,z)+ax,Q(z)+by, cz+d), $$ where $P$ and $Q$ are polynomials with $\max\{\deg(P),\deg(Q)\}=2$ and $abc\ne 0$.

    (iii) $$ \cases H_1(x,y,z)=(P(x,z)+ay,Q(z)+x,cz+d)\\ H_2(x,y,z)=(P(y,z)+ax,Q(y)+bz,y)\\ H_3(x,y,z)=(P(x,z)+ay,Q(x)+z,x)\\ H_4(x,y,z)=(P(x,y)+az,Q(y)+x,y)\\ H_5(x,y,z)=(P(x,y)+az,Q(x)+by,x) \endcases $$ where $P$ and $Q$ are polynomials with $\max\{\deg(P),\deg(Q)\}=2$ and $abc\ne 0$.