# Smooth contractible threefolds with hyperbolic $$\mathbb {G}_{m}$$ G m -actions via polyhedral divisors

Smooth contractible threefolds with hyperbolic $$\mathbb {G}_{m}$$ G m -actions via... The aim of this note is to give an alternative proof of the Theorem 4.1 of Koras and Russell (J Algebr Geom 6(4): 671–695, 1997), that is, a characterization of smooth contractible affine varieties endowed with a hyperbolic action of the group $$\mathbb {G}_{m}\simeq \mathbb {C}^{\text {*}}$$ G m ≃ C * , using the language of polyhedral divisors developed in Altmann and Hausen (Math Ann 334:557–607, 2006) as generalization of $$\mathbb {Q}$$ Q -divisors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

# Smooth contractible threefolds with hyperbolic $$\mathbb {G}_{m}$$ G m -actions via polyhedral divisors

, Volume 156 (4) – Sep 11, 2017
10 pages

/lp/springer_journal/smooth-contractible-threefolds-with-hyperbolic-mathbb-g-m-g-m-actions-UyIhzqFySo
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
D.O.I.
10.1007/s00229-017-0972-1
Publisher site
See Article on Publisher Site

### Abstract

The aim of this note is to give an alternative proof of the Theorem 4.1 of Koras and Russell (J Algebr Geom 6(4): 671–695, 1997), that is, a characterization of smooth contractible affine varieties endowed with a hyperbolic action of the group $$\mathbb {G}_{m}\simeq \mathbb {C}^{\text {*}}$$ G m ≃ C * , using the language of polyhedral divisors developed in Altmann and Hausen (Math Ann 334:557–607, 2006) as generalization of $$\mathbb {Q}$$ Q -divisors.

### Journal

Manuscripta MathematicaSpringer Journals

Published: Sep 11, 2017

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