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

作者：Langlois Kevin; Liendo Alvaro^*

来源：Journal of Algebra, 2016, 449: 730-773.

DOI：10.1016/j.jalgebra.2015.11.019

• Torus actions
• Locally finite iterative higher derivations
• Affine varieties

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.

• 出版日期2016-3-1