Unipotent group actions on affine varieties

2010/02/22 by Derksen, Harm, Essen, Arno van den, Finston, David R. +1
#14L17 #14L24 #14L30 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1002.4181

Abstract

Algebraic actions of unipotent groups U actions on affine k-varieties X (k an algebraically closed field of characteristic 0) for which the algebraic quotient X//U has small dimension are considered. In case X is factorial, O(X)^∗=k^∗, and X//U is one-dimensional, it is shown that O(X)^U=k[f], and if some point in X has trivial isotropy, then X is U equivariantly isomorphic to U× A¹(k). The main results are given distinct geometric and algebraic proofs. Links to the Abhyankar-Sathaye conjecture and a new equivalent formulation of the Sathaye conjecture are made.

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