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Embeddings of SL(2,Z) into the Cremona group

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arxiv 1103.0114 v2 pith:QSG245KS submitted 2011-03-01 math.AG math.GR

Jérémy Blanc , Julie Déserti This is my paper
classification math.AGmath.GR
keywords embeddingsgroupelementselliptichyperboliccremonainfinitelymany
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Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate 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.

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