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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 : 2016-07-25
Accepté le : 2017-07-24
Publié le : 2019-12-09
DOI : https://doi.org/10.5802/afst.1614
Classification : 37P45,  37P05
Mots clés: dynamical moduli space
@article{AFST_2019_6_28_4_733_0,
     author = {Michelle Manes and Joseph H. Silverman},
     title = {A classification of degree~$2$ semi-stable rational maps $\protect \mathbb{P}^2\rightarrow \protect \mathbb{P}^2$ with large finite dynamical automorphism group},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {4},
     year = {2019},
     pages = {733-811},
     doi = {10.5802/afst.1614},
     language = {en},
     url = {afst.centre-mersenne.org/item/AFST_2019_6_28_4_733_0/}
}
Michelle Manes; Joseph H. Silverman. 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. https://afst.centre-mersenne.org/item/AFST_2019_6_28_4_733_0/

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