On restriction of roots on affine \(T\)-varieties

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Abstract

Let \(X\) be a normal affine algebraic variety with a regular action of a torus \(\mathbb {T}\) and \(T\subset \mathbb {T}\) be a subtorus. We prove that each root of \(X\) with respect to \(T\) can be obtained by restriction of some root of \(X\) with respect to \(\mathbb {T}\). This allows to give an elementary proof of the description of roots of the affine Cremona group. Several results on restriction of roots in the case of a subtorus action on an affine toric variety are obtained.

Keywords

Locally nilpotent derivation Torus action Roots of an algebraic group Affine Cremona group Toric surface 

Mathematics Subject Classification

14R10 14R20 14L30 14M25 13N15 
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Notes

Acknowledgments

The author is grateful to I.V. Arzhantsev for posing the problem and permanent support. Thanks are also due to A. Liendo for useful comments.

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Copyright information

© The Managing Editors 2013

Authors and Affiliations

  1. 1.Department of Higher Algebra, Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia

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