2008/12/31 by Alvaro Liendo · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Affine transformation #Affine variety #Algebraic Geometry and Number Theory #Algebraically closed field #Combinatorics #Dimension (graph theory) #Discrete mathematics #Geometry #Homogeneous #Invariant (physics) #Locally nilpotent #Mathematics #Nilpotent #Nilpotent group #Pure mathematics #Torus #math.AG #msc:13N15 #msc:14M25 #msc:14R05 #msc:14R20
paper · pdf · doi:10.1007/s00031-010-9089-2
published as Transformation Groups: Vol. 15, No. 2, 2010, pp 389-425 · 31 pages. Minor changes in the structure. Fixed some typos
openalex publication_date 2010/04/07 · arxiv created 2011/02/04 · arxiv updated 2015/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Zn-graded domain A, so that D generates a k+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=dim X) and in the case where n=dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.