EQUIVARIANTLY UNIFORMLY RATIONAL VARIETIES

Abstract : Abstract. We introduce equivariant versions of uniform rationality: given an algebraic group G, a G-variety is called G-uniformly rational (resp. G-linearly uniformly rational) if every point has a G-invariant open neighborhood equivariantly isomorphic to a G-invariant open subset of the affine space endowed with a G-action (resp. linear G-action). We establish a criterion for Gm-uniform rationality of affine variety equipped with hyperbolic Gm-action with a unique fixed point, formulated in term of their Altmann-Hausen presentation. We prove the Gm-uniform rationality of Koras-Russel threefolds of the first kind and we also give example of non Gm-uniformly rational but smooth rational Gm-threefold associated to pairs of plane rational curves birationally non equivalent to a union of lines.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01151427
Contributeur : Charlie Petitjean <>
Soumis le : mardi 12 mai 2015 - 19:54:57
Dernière modification le : mardi 12 janvier 2016 - 12:58:02
Document(s) archivé(s) le : mercredi 19 avril 2017 - 22:50:32

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  • HAL Id : hal-01151427, version 1

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Charlie Petitjean. EQUIVARIANTLY UNIFORMLY RATIONAL VARIETIES. 2015. <hal-01151427>

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