% Encoding: UTF-8
@COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/}
@COMMENT{For any questions please write to cris-support@fau.de}
@article{faucris.123076844,
abstract = {Let G be a reductive group defined over an algebraically closed field k and let X be a G-variety. In this paper we study G-invariant valuations v of the field K of rational functions on X. These objects are fundamental for the theory of equivariant completions of X. Let B be a Borel subgroup and U the unipotent radical of B. It is proved that v is uniquely determined by its restriction to K(U). Then we study the set of invariant valuations having some fixed restriction v0 to K(B). If V0 is geometric (i.e., induced by a prime divisor) then this set is a polyhedron in some vector space. In characteristic zero we prove that this polyhedron is a simplicial cone and in fact the fundamental domain of finite reflection group W(X). Thus, the classification of invariant valuations is almost reduced to the classification of valuations of K(B).},
author = {Knop, Friedrich},
doi = {10.1007/BF01444891},
faupublication = {no},
journal = {Mathematische Annalen},
pages = {333-363},
peerreviewed = {Yes},
title = {{Über} {Bewertungen}, welche unter einer reduktiven {Gruppe} invariant sind},
volume = {295},
year = {1993}
}