Tame Automorphisms of $\Bbb{C}^{3}$ with Multidegree of the Form $(p_{1},p_{2},d_{3})$

Marek Karaś¹

¹ Instytut Matematyki Uniwersytetu Jagiellońskiego Łojasiewicza 6 30-348 Kraków, Poland

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 27-32.

Résumé

Let $d_{3}\geq p_{2}>p_{1}\geq 3$ be integers such that $p_{1},p_{2}$ are prime numbers. We show that the sequence $(p_{1},p_{2},d_{3})$ is the multidegree of some tame automorphism of $\mathbb{C}^{3}$ if and only if $d_{3}\in p_{1}\Bbb{N}+p_{2}\Bbb{N},$ i.e. if and only if $d_{3}$ is a linear combination of $p_{1}$ and $p_{2}$ with coefficients in $\mathbb{N}.$

Détail

DOI : 10.4064/ba59-1-4

Keywords: geq geq integers prime numbers sequence multidegree tame automorphism mathbb only bbb bbb only linear combination coefficients nbsp mathbb