Algebraic subgroups of the plane Cremona group over a perfect field

Finite abelian subgroups of the Cremona group of the plane

Maximal Algebraic Subgroups of the Cremona Group of Three Variables Imprimitive Algebraic Subgroups of Exceptional Type

Enriques and Fano [4], [5] classified all the maximal connected algebraic subgroups of Cr3. Our aim is to give modern and rigorous proofs to their results. In [10], we studied the primitive subgroups. In this paper, we deal with exceptional imprimitive groups. The imprimitivity is an analytic notion. The natural translation of the imprimitivity in algebraic geometry is the de Jonquieres type op...

Linearisation of Finite Abelian Subgroups of the Cremona Group of the Plane

This article gives the proof of results announced in [Bla07a] and some description of automorphisms of rational surfaces. Given a finite abelian subgroup of the Cremona group of the plane, we give a way to decide whether this one is birationally conjugate to a group of automorphisms of a minimal surface. In particular, we prove that a finite cyclic group of birational transformations of the pla...

Nonlinearity of Some Subgroups of the Planar Cremona Group

We give some examples of nonlinear subgroups of the planar Cremona group.

The Cremona group of the plane is compactly presented

This article shows that the Cremona group of the plane is compactly presented. To do this we prove that it is a generalised amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one relation.