Holomorphic diffeomorphisms of semisimple homogeneous spaces

Árpád Tóth; Dror Varolin

doi:10.1112/S0010437X06002077

Holomorphic diffeomorphisms of semisimple homogeneous spaces

Árpád Tóth
, Dror Varolin

Mathematics

Eötvös Loránd University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1308-1326
Number of pages	19
Journal	Compositio Mathematica
Volume	142
Issue number	5
DOIs	https://doi.org/10.1112/S0010437X06002077
State	Published - 2006

Keywords

Automorphism groups of affine manifolds
Complex vector fields
Homogeneous complex manifolds
Semisimple Lie groups and their representations

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10.1112/S0010437X06002077

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abstract = "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.",

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AU - Tóth, Árpád

AU - Varolin, Dror

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N2 - 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.

AB - 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.

KW - Automorphism groups of affine manifolds

KW - Complex vector fields

KW - Homogeneous complex manifolds

KW - Semisimple Lie groups and their representations

UR - https://www.scopus.com/pages/publications/33845345233

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DO - 10.1112/S0010437X06002077

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SP - 1308

EP - 1326

JO - Compositio Mathematica

JF - Compositio Mathematica

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Holomorphic diffeomorphisms of semisimple homogeneous spaces

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Keywords

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