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Good quotients for actions of Sl(2). (English) Zbl 0780.14024

Summary: Let a reductive group \(G\) act on a normal algebraic variety \(X\). It is known that if there exists a geometric quotient \(X\to X/T\) for any one- dimensional torus \(T\subseteq G\), then there exists a geometric quotient \(X\to X/G\) (where \(X/G\) is an algebraic space). In this paper we prove the analogous result for good quotients in case \(G=\)Sl(2). However, it seems that the methods used here can be generalized to give an analogous result for all reductive groups \(G\). Proofs of some auxiliary results are only sketched. Hence the present paper can be considered as a preliminary version of a more general result [cf. the authors, Am. J. Math. 113, No. 2, 189-201 (1991; Zbl 0741.14031)].

MSC:

14M17 Homogeneous spaces and generalizations
14L30 Group actions on varieties or schemes (quotients)

Citations:

Zbl 0741.14031
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