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Automorphismes loxodromiques de surfaces abéliennes réelles
ShengYuan Zhao1
1 Université de Rennes I, Campus de Beaulieu, Bâtiment 22-23, 263 avenue du Général Leclerc, Rennes (France)
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 1, pp. 109-127.

We study dynamical degree >1 real automorphisms of compact complex surfaces with a real structure. We show that a surface with such an automorphism is necessarily projective. We classify real abelian surfaces into eight types, according to the number of connected components of the real part and the simplicity of the underlying complex abelian surface. For each type, we determine the set of values of dynamical degrees which can be realized by real automorphisms. We also prove that the minimum dynamical degree on a complex K3 surface can not be realized on a real K3 surface.

On étudie les automorphismes réels de degré dynamique >1 des surfaces complexes compactes munies d’une structure réelle. On montre qu’une surface possédant un tel automorphisme est projective. On classifie des surfaces abéliennes réelles en huit types, selon le nombre de composantes connexes de la partie réelle et la simplicité de la surface abélienne complexe sous-jacente. Pour chacun des huit types, on détermine l’ensemble des valeurs de degrés dynamiques qui peuvent être réalisées par des automorphismes réels. On montrera aussi que le degré dynamique minimum sur une surface K3 complexe ne peut pas être réalisée sur une surface K3 réelle.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1595

ShengYuan Zhao 1

1 Université de Rennes I, Campus de Beaulieu, Bâtiment 22-23, 263 avenue du Général Leclerc, Rennes (France)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {ShengYuan Zhao},
     title = {Automorphismes loxodromiques de surfaces ab\'eliennes r\'eelles},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {109--127},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 28},
     number = {1},
     year = {2019},
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ShengYuan Zhao. Automorphismes loxodromiques de surfaces abéliennes réelles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 1, pp. 109-127. doi : 10.5802/afst.1595. https://afst.centre-mersenne.org/articles/10.5802/afst.1595/

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