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

作者：Blanc Jeremy^*; Deserti Julie

来源：Transformation Groups, 2012, 17(1): 21-50.

DOI：10.1007/s00031-012-9174-9

Geometric and dynamic properties of embeddings of SL(2; a%26quot;currency sign) 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; a%26quot;currency sign), preserves an elliptic curve and all its elements of infinite order are hyperbolic.

• 出版日期2012-3