Automorphism Groups of Moishezon Threefolds (original) (raw)

Automorphism groups of certain rational hypersurfaces in complex four-space

2013

The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences of this structure and generalize some results to other hypersurfaces which arise as deformations of Koras-Russell threefolds.

Jordan Properties of Automorphism Groups of Certain Open Algebraic Varieties

Transformation Groups, 2018

Let W be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that W is birational to a product of a smooth projective variety A and the projective line. We prove that if A contains no rational curves then the automorphism group G := Aut(W) of W is Jordan. That means that there is a positive integer J = J(W) such that every finite subgroup B of G contains a commutative subgroup A such that A is normal in B and the index [B : A] ≤ J .

Three-dimensional connected groups of automorphisms of toroidal circle planes

Advances in Geometry, 2019

We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to PSL(2, ℝ). Using this result, we describe a framework for the full classification based on the action of the group on the point set.

Jordan Groups and Algebraic Surfaces

Transformation Groups, 2014

We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of

Planar groups of automorphisms of stable planes

Journal of Geometry, 1992

Semi-) planar groups of stable planes are introduced, and information about their size and their structure is derived. A special case are the stabilizers of quadrangles in compact connected projective planes (i.e. automorphism groups of locally compact connected ternary fields). 1. INTRODUCTION.

Automorphism groups of complex doubles of Klein surfaces

Glasgow Mathematical Journal, 1994

In this paper we consider complex doubles of compact Klein surfaces that have large automorphism groups. It is known that a bordered Klein surface of algebraic genus g > 2 has at most 12(g − 1) automorphisms. Surfaces for which this bound is sharp are said to have maximal symmetry. The complex double of such a surface X is a compact Riemann surface X+ of genus g and it is easy to see that if G is the group of automorphisms of X then C2 × G is a group of automorphisms of X+. A natural question is whether X+ can have a group that strictly contains C2 × G. In [8] C. L. May claimed the following interesting result: there is a unique Klein surface X with maximal symmetry for which Aut X+ properly contains C2 × Aut X (where Aut X+ denotes the group of conformal and anticonformal automorphisms of X+).