The Kempf-ness Theorem and Invariant Theory
نویسنده
چکیده
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
منابع مشابه
Moment Maps and Geometric Invariant Theory
These are expanded notes from a set of lectures given at the school “Actions Hamiltoniennes: leurs invariants et classification” at Luminy in April 2009. The topics center around the theorem of Kempf and Ness [58], which describes the equivalence between the notion of quotient in geometric invariant theory introduced by Mumford in the 1960’s [80], and the notion of symplectic quotient introduce...
متن کاملToric Kempf–Ness sets
In the theory of algebraic group actions on affine varieties, the concept of a Kempf– Ness set is used to replace the categorical quotient by the quotient with respect to a maximal compact subgroup. Using recent achievements of “toric topology,” we show that an appropriate notion of a Kempf–Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate subspace arra...
متن کاملTopology of Kempf–Ness sets for algebraic torus actions
In the theory of algebraic group actions on affine varieties, the concept of a Kempf–Ness set is used to replace the geometric quotient by the quotient with respect to a maximal compact subgroup. By making use of the recent achievements of “toric topology” we show that an appropriate notion of a Kempf–Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate su...
متن کاملStratifications Associated to Reductive Group Actions on Affine Spaces
For a complex reductive group G acting linearly on a complex affine space V with respect to a characterρ, we show two stratifications ofV associated to this action (and a choice of invariant inner product on the Lie algebra of the maximal compact subgroup ofG) coincide. The first is Hesselink’s stratification by adapted 1-parameter subgroups and the second is the Morse theoretic stratification ...
متن کاملGeometric Reductivity at Archimedean Places
Let G → GL(n,C) be a representation of a complex reductive group. A theorem of Hilbert says that the algebra C[x1, . . . , xn] of invariant polynomials is finitely generated. Let Y be the projective variety defined by this graded algebra, and then we have a rational morphism π : C · · · → Y(C). A theorem on geometric reductivity of Mumford says that a point x ∈ C is regular for the map π if and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006