Search results for "Hyperbolic torus action"

Hyperbolic actions of the multiplicative group on affine varieties : exotic spaces and local structures

2015

This thesis is devoted to the study of affine T-varieties using the Altmann-Hausen presentation. We are especially interested in the case of hyperbolic actions of the multiplicative group Gm. In the first part, exotic affine spaces are studied, that is, smooth contractible affine varieties, assuming in addition that they are endowed with a Gm-action. In particular, in the case of dimension 3, we reinterpret the construction of Koras-Russell threefolds in terms of polyhedral divisors andwe give constructions of smooth contractible affine varieties and in dimensionslarger than 3.In the second part we consider the property of G-uniform rationality for a G-variety. This means that every point o…