0000000000987798

AUTHOR

Charlie Petitjean

showing 2 related works from this author

Cyclic covers of affine T-varieties

2015

Abstract We consider normal affine T -varieties X endowed with an action of finite abelian group G commuting with the action of T . For such varieties we establish the existence of G-equivariant geometrico-combinatorial presentations in the sense of Altmann and Hausen. As an application, we determine explicit presentations of the Koras–Russell threefolds as bi-cyclic covers of A 3 equipped with a hyperbolic G m -action.

Pure mathematicsAlgebra and Number TheoryAffine transformationAbelian groupAction (physics)MathematicsJournal of Pure and Applied Algebra
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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…

[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]G-uniformément rationnelleVariétés de Koras-Russell[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]T-variétés[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Koras-Russell threefoldsHyperbolic torus actionT-varietiesG-uniformly rationalAction hyperbolique du tore
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