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

Abstract

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.

to appear in Transformation Groups

References in corpus (4)

• On the inertia group of elliptic curves in the Cremona group of the plane
• Sur un théorème de Castelnuovo
• On Birational Transformations of Pairs in the Complex Plane
• Algebraic stability and degree growth of monomial maps and polynomial maps

Cited by in corpus (2)

• Sofic profile and computability of Cremona groups
• Infinitesimal deformations of rational surface automorphisms