Additive group actions on affine T-varieties of complexity one in arbitrary characteristic

JOURNAL OF ALGEBRA

卷:449

Article

Langlois, Kevin¹  Liendo, Alvaro² 

[1] Max Planck Inst Math, Gottfried Claren Str 26, D-53111 Bonn, Germany

[2] Univ Talca, Inst Matemat & Fis, Casilla 721, Talca, Chile

关键词: Torus actions;    Locally finite iterative higher derivations;    Affine varieties;   

DOI  :  10.1016/j.jalgebra.2015.11.019

来源: Elsevier

【 摘 要 】

Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T = G(m)(n), stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This generalizes the classification given by the second author in the particular case where k is algebraically closed and of characteristic zero. With the assumption that the characteristic of k is positive, we introduce the notion of rationally homogeneous locally finite iterative higher derivations which corresponds geometrically to additive group actions on affine T-varieties normalized up to a Frobenius map. As a preliminary result, we provide a complete description of these G(a)-actions in the toric situation. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free