P. Russell and M. Koras classified all smooth affine contractible three-folds with hyperbolic C-action and quotient isomorphic to that of the corresponding linear action on the tangent space at the unique fixed point. It is not clear from their description whether there exist nontrivial Russell-Koras threefolds that are isomorphic to C3. They showed that this question arises naturally in connection with the problem of linearizing a C-action on C3. We prove that none of the nontrivial Russell-Koras threefolds are isomorphic to C3.
|Original language||English (US)|
|Number of pages||22|
|Journal||Journal of Algebraic Geometry|
|State||Published - Dec 1 1997|
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology