On Automorphisms of the Affine Cremona Group

Cremona Transformations, Surface Automorphisms and the Group Law

We give a method for constructing many examples of automorphisms with positive entropy on rational complex surfaces. The general idea is to begin with a quadratic cremona transformation that fixes some cubic curve and then use the group law to understand when the indeterminacy and exceptional behavior of the transformation may be eliminated by repeated blowing up.

Blanc Conjugacy classes of affine automorphisms of K n and linear automorphisms of P n in the Cremona groups

Let K be an algebraically closed field of characteristic 0 and let K and P denote respectively the affine and projective n-spaces over K. The Cremona group, which is the group of birational maps of these two spaces,Bir(K) = Bir(P), has been studied a lot, especially in dimension 2 and 3, see for example [Hud] and [AlC]. Its subgroup of biregular morphisms (or automorphisms) of K, called the aff...

On Marginal Automorphisms of a Group Fixing the Certain Subgroup

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...

Cremona Transformations, Surface Automorphisms, and Plane Cubics

Every automorphism of the complex projective plane P2 is linear and therefore behaves quite simply when iterated. It is natural to seek other rational complex surfaces—for instance, those obtained from P2 by successive blowing up—that admit automorphisms with more interesting dynamics. Until recently, very few examples with positive entropy seem to have been known (see e.g. the introduction to ...

ON POLYNOMIAL AUTOMORPHISMS OF AFFINE SPACESVladimir