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We classify simple groups that act by birational transformations on compact complex Kahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrary field is finite.
We improve a result of Prokhorov and Shramov on the rank of finite $p$-subgroups of the birational automorphism group of a rationally connected variety. Known examples show that they are sharp in many cases.
A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear system of degre
We prove a generalization of Shafarevichs Conjecture for fields of Laurent series in two variables over an arbitrary field. While not projective, the absolute Galois group of such a field is shown to be semi-free. We also show that the function field
We look at sequences of positive integers that can be realized as degree sequences of iterates of rational dominant maps of smooth projective varieties over arbitrary fields. New constraints on the degree growth of endomorphisms of the affine space a
In this paper, we study distortion in the group $mathcal A$ of Affine Interval Exchange Transformations (AIET). We prove that any distorted element $f$ of $mathcal A$, has an iterate $f^ k$ that is conjugate by an element of $mathcal A$ to a product