Stability of Affine G-varieties and Irreducibility in Reductive Groups
نویسنده
چکیده
Let G be a reductive affine algebraic group, and let X be an affine algebraic G-variety. We establish a (poly)stability criterion for points x ∈ X in terms of intrinsically defined closed subgroups Hx of G, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-Röhrle criteria, in the caseX = G . Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.
منابع مشابه
Stable Reductive Varieties I: Affine Varieties
0. Introduction 1 1. Main definitions and results 3 2. General criteria 6 2.1. Seminormality and connectedness of isotropy groups 6 2.2. Finiteness of number of orbits and group–like condition 9 3. Orbits in stable reductive varieties 11 3.1. Isotropy groups 11 3.2. Algebras of regular functions 14 4. Reductive varieties 18 4.1. Classification 18 4.2. Associated stable toric varieties 20 5. Sta...
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