Displaying similar documents to “On complete orbit spaces of SL(2) actions, II”

A Hilbert-Mumford criterion for SL₂-actions

Jürgen Hausen (2003)

Colloquium Mathematicae

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Let the special linear group G : = SL₂ act regularly on a ℚ-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U ⃫N with a divisorial quotient space, then the intersection W(U) of all translates g · U is open in X and admits a good quotient W(U) → W(U) ⃫G with a divisorial quotient space. Conversely, we show that every maximal open G-invariant subset W ⊂ X admitting a good...

A general Hilbert-Mumford criterion

Jürgen Hausen (2003)

Annales de l’institut Fourier

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Let a reductive group G act on an algebraic variety X . We give a Hilbert-Mumford type criterion for the construction of open G -invariant subsets V ⊂ X admitting a good quotient by G .

A combinatorial construction of sets with good quotients by an action of a reductive group

Joanna Święcicka (2001)

Colloquium Mathematicae

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The aim of this paper is to construct open sets with good quotients by an action of a reductive group starting with a given family of sets with good quotients. In particular, in the case of a smooth projective variety X with Pic(X) = 𝒵, we show that all open sets with good quotients that embed in a toric variety can be obtained from the family of open sets with projective good quotients. Our method applies in particular to the case of Grassmannians.

On actions of ℂ * on algebraic spaces

Andrzej Bialynicki-Birula (1993)

Annales de l'institut Fourier

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The main result of the paper says that all schematic points of the source of an action of C * on an algebraic space X are schematic on X .