A classification of degree 2 semi-stable rational maps 2 2 with large finite dynamical automorphism group
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 4, pp. 733-811.

Soit K un corps algébriquement clos de charactéristique 0. Dans cet article nous classifions les PGL 3 (K)-classes de conjugaison de fonctions rationelles f: K 2 K 2 de degré 2 dominantes et semi-stables dont le groupe d’automorphismes

Aut(f):={φPGL3(K):φ-1fφ=f}

est fini et d’ordre au moins 3. En particulier, nous démontrons que #Aut(f)24 en général, que #Aut(f)21 pour les morphismes et que #Aut(f)6 pour toutes excepté un nombre fini de classes de conjugaisons de f.

Let K be an algebraically closed field of characteristic 0. In this paper we classify the PGL 3 (K)-conjugacy classes of semi-stable dominant degree 2 rational maps f: K 2 K 2 whose automorphism group

Aut(f):={φPGL3(K):φ-1fφ=f}

is finite and of order at least 3. In particular, we prove that #Aut(f)24 in general, that #Aut(f)21 for morphisms, and that #Aut(f)6 for all but finitely many conjugacy classes of f.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1614
Classification : 37P45, 37P05
Mots clés : dynamical moduli space
Manes, Michelle 1 ; Silverman, Joseph H. 2

1 Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA
2 Mathematics Department, Box 1917 Brown University, Providence, RI 02912, USA
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Manes, Michelle; Silverman, Joseph H. A classification of degree $2$ semi-stable rational maps $\protect \mathbb{P}^2\rightarrow \protect \mathbb{P}^2$ with large finite dynamical automorphism group. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 4, pp. 733-811. doi : 10.5802/afst.1614. http://archive.numdam.org/articles/10.5802/afst.1614/

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