Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus
نویسندگان
چکیده
منابع مشابه
Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus
Consider an algebraic action of a connected complex reductive algebraic group on a complex polarized projective variety. In this paper, we first introduce the nilpotent quotient, the quotient of the polarized projective variety by a maximal unipotent subgroup. Then, we introduce and investigate three induced actions: one by the reductive group, one by a Borel subgroup, and one by a maximal toru...
متن کاملQuotients by non-reductive algebraic group actions
Geometric invariant theory (GIT) was developed in the 1960s by Mumford in order to construct quotients of reductive group actions on algebraic varieties and hence to construct and study a number of moduli spaces, including, for example, moduli spaces of bundles over a nonsingular projective curve [26, 28]. Moduli spaces often arise naturally as quotients of varieties by algebraic group actions,...
متن کاملGeometric Quotients of Unipotent Group Actions
This article is devoted to the problem of constructing geometric quotients of a quasiaffine scheme X over a field of characteristic 0 by a unipotent algebraic group G. This problem arises naturally if one tries to construct moduli spaces in the sense of Mumford's 'geometric invariant theory' for singularities of algebraic varieties or for modules over the local ring of such a singularity. Indee...
متن کاملSymplectic quotients by a nonabelian group and by its maximal torus
This paper examines the relationship between the symplectic quotientX//G of a Hamiltonian G-manifold X , and the associated symplectic quotient X//T , where T ⊂ G is a maximal torus, in the case in which X//G is a compact manifold or orbifold. The three main results are: a formula expressing the rational cohomology ring of X//G in terms of the rational cohomology ring of X//T ; an ‘integration’...
متن کاملActions of the Derived Group of a Maximal Unipotent Subgroup on G-varieties
The ground field k is algebraically closed and of characteristic zero. Let G be a semisimple simply-connected algebraic group over k and U a maximal unipotent subgroup of G. One of the fundamental invariant-theoretic facts, which goes back to Hadžiev [9], is that k[G/U ] is a finitely generated k-algebra and regarded as G-module it contains every finite-dimensional simple G-module exactly once....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2006
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2006.v2.n4.a9