Knop F (1993)
Publication Language: German
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1993
Publisher: Springer Verlag (Germany)
Book Volume: 295
Pages Range: 333-363
Journal Issue: 2
DOI: 10.1007/BF01444891
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).
APA:
Knop, F. (1993). Über Bewertungen, welche unter einer reduktiven Gruppe invariant sind. Mathematische Annalen, 295(2), 333-363. https://doi.org/10.1007/BF01444891
MLA:
Knop, Friedrich. "Über Bewertungen, welche unter einer reduktiven Gruppe invariant sind." Mathematische Annalen 295.2 (1993): 333-363.
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