The separating variety for the basic representations of the additive group

JOURNAL OF ALGEBRA

卷:377

Article

Dufresne, Emilie¹  Kohls, Martin² 

[1] Univ Basel, Math Inst, CH-4051 Basel, Switzerland

[2] Tech Univ Munich, Zentrum Math M11, D-85748 Garching, Germany

关键词: Invariant theory;    Separating invariants;    Locally nilpotent derivations;    Basic actions;    Weitzenbock derivations;   

DOI  :  10.1016/j.jalgebra.2012.11.043

来源: Elsevier

【 摘 要 】

For a group G acting on an affine variety X, the separating variety is the closed subvariety of X x X encoding which points of X are separated by invariants. We concentrate on the indecomposable rational linear representations V-n of dimension n + 1 of the additive group of a field of characteristic zero, and decompose the separating variety into the union. of irreducible components. We show that if n is odd, divisible by four, or equal to two, the closure of the graph of the action, which has dimension n + 2, is the only component of the separating variety. In the remaining cases, there is a second irreducible component of dimension n + 1. We conclude that in these cases, there are no polynomial separating algebras. (C) 2012 Published by Elsevier Inc.

【 授权许可】

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