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Holomorphic diffeomorphisms of semisimple homogeneous spaces

Published online by Cambridge University Press:  25 September 2006

Árpád Tóth  and
Dror Varolin
Árpád Tóth
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter 1/c, Hungarytoth@cs.elte.hu
Dror Varolin
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USAdror@math.sunysb.edu
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Abstract

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We study the infinite-dimensional group of holomorphic diffeomorphisms of certain Stein homogeneous spaces. We show that holomorphic automorphisms can be approximated by generalized shears arising from unipotent subgroups. For the homogeneous spaces this implies the existence of Fatou–Bieberbach domains of the first and second kind, and the failure of the Abhyankar–Moh theorem for holomorphic embeddings.

Keywords

homogeneous complex manifoldsautomorphism groups of affine manifoldscomplex vector fieldssemisimple Lie groups and their representations32M0532M1732M2522E46
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1308 - 1326
Copyright
Foundation Compositio Mathematica 2006