A generalization of Mumford's geometric invariant theory.
Hausen, Jürgen (2001)
Documenta Mathematica
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Hausen, Jürgen (2001)
Documenta Mathematica
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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...
Olga Chuvashova, Nikolay Pechenkin (2013)
Open Mathematics
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Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on...
Reichstein, Zinovy, Vonessen, Nikolaus (2004)
Journal of Lie Theory
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Dmitri I. Panyushev (1995)
Annales de l'institut Fourier
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We study -actions of the form , where is the dual (to ) -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action is given. It is shown that the doubled actions have a number of nice properties, if is spherical or of complexity one.
Haruhisa Nakajima (1995)
Annales de l'institut Fourier
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Let be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on compatible with the conical structure. We show that such actions are cofree and the nullcones of associated with them are complete intersections.
Ivan V. Arzhantsev (2003)
Annales de l’institut Fourier
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We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.
Hanspeter Kraft (1994-1995)
Séminaire Bourbaki
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