Free C_+ -actions on C^3 are translations
Abstract
Let X' be a smooth contractible three-dimensional affine algebraic variety with a free algebraic C_+ -action on it such that S =X'// C_+ is smooth. We prove that X' is isomorphic to $S \times \C$ and the action is induced by a translation on the second factor. As a consequence we show that any free algebraic C_+ -action on C^3 is a translation in a suitable coordinate system.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 2002
- DOI:
- 10.48550/arXiv.math/0207156
- arXiv:
- arXiv:math/0207156
- Bibcode:
- 2002math......7156K
- Keywords:
-
- Algebraic Geometry;
- 14R20;
- 14R10
- E-Print:
- 12 pages