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Embeddings of SL(2; ℤ) into the cremona group

BLANC, JÉRÉMY ; DÉSERTI, JULIE

In: Transformation Groups, 2012, vol. 17, no. 1, p. 21-50

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    Titre
    • Embeddings of SL(2; ℤ) into the cremona group
    Auteur
    • BLANC, JÉRÉMY. Universität Basel Mathematisches Institut, Rheinsprung 21, CH-4051, Basel, Switzerland
    • DÉSERTI, JULIE. Universität Basel Mathematisches Institut, Rheinsprung 21, CH-4051, Basel, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Transformation Groups, 2012, vol. 17, no. 1, p. 21-50. SP Birkhäuser Verlag Boston
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:317035
    Summary
    Geometric and dynamic properties of embeddings of SL(2; ℤ) into the Cremona group are studied. Infinitely many nonconjugate embeddings that preserve the type (i.e., that send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many nonconjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2; ℤ), preserves an elliptic curve and all its elements of infinite order are hyperbolic