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Reductive group actions on affine varieties and their doubling. (English) Zbl 0831.14022
Summary: We study \(G\)-actions of the form \((G:X\times X^{*})\), where \(X^{*}\) is the \(G\)-variety dual to \(X\). These actions are called doubled ones. A geometric interpretation of the complexity of the action \((G:X)\) is given. It is shown that the doubled actions have a number of nice properties, if \(X\) is spherical or of complexity one.

MSC:
14L30 Group actions on varieties or schemes (quotients)
13A50 Actions of groups on commutative rings; invariant theory
14L24 Geometric invariant theory
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