The computation of invariant fields and a constructive version of a theorem by rosenlicht

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Abstract

Let G be an algebraic group acting on an irreducible variety X. We present an algorithm for computing the invariant field k(X)G. Moreover, we give a constructive version of a theorem of Rosenlicht, which says that almost all orbits can be separated by rational invariants. More precisely, we give an algorithm for computing a nonempty open subset of X with a geometric quotient.

Original languageEnglish
Pages (from-to)657-670
Number of pages14
JournalTransformation Groups
Volume12
Issue number4
DOIs
StatePublished - Dec 2007

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