Stability of Affine G-varieties and Irreducibility in Reductive Groups

نویسنده

  • ANA CASIMIRO
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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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...

متن کامل

Computation of Weyl Groups of G-varieties

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for homogeneous spaces and affine homogeneous vector bundles. For some special classes of G-varieties (affine...

متن کامل

Lecture 1: Nakajima Quiver Varieties

Recall that an algebraic group G is called (linearly) reductive if any its rational (i.e., algebraic) representation is completely reducible. The finite groups, the group GLn and the products GLn1 × . . .GLnk are reductive. Below G denotes a reductive algebraic group and X is an affine algebraic variety equipped with an (algebraic) action of G. Results explained below in this section can be fou...

متن کامل

Equivariant Vector Bundles on Certain Affine G-Varieties

We give a concrete description of the category of G-equivariant vector bundles on certain affine G-varieties (where G is a reductive linear algebraic group) in terms of linear algebra data.

متن کامل

Classification of Smooth Affine Spherical Varieties

Let G be a complex reductive group. A normal G-variety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian Kmanifolds, K a maximal compact subgroup of G. In this paper, we classify all smooth affine spherical varieties up to coverings, cent...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012