Newton polytopes of invariants of additive group actions

It is shown that the vertices of Newton polytopes of invariants of an algebraic group action of the additive group of a field k of arbitrary characteristic on affine n-space over k lie on the coordinate hyperplanes. Furthermore, let E be the set of all edges of these Newton polytopes whose vertices...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2001-02, Vol.156 (2), p.187-197
Main Authors: Derksen, Harm, Hadas, Ofer, Makar-Limanov, Leonid
Format: Article
Language:English
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Summary:It is shown that the vertices of Newton polytopes of invariants of an algebraic group action of the additive group of a field k of arbitrary characteristic on affine n-space over k lie on the coordinate hyperplanes. Furthermore, let E be the set of all edges of these Newton polytopes whose vertices lie in different coordinate hyperplanes. It is shown that one of these polytopes has edges with all directions represented in E.
ISSN:0022-4049
1873-1376
DOI:10.1016/S0022-4049(99)00151-6