Projectivity of Moment Map Quotients
نویسنده
چکیده
Let G be a complex reductive group acting algebraically on a complex projective variety X . Given a polarisation of X , i.e., an ample G-line bundle L over X , Mumford (see [M-F-K]) defined the notion of stability: A point x ∈ X is said to be semistable with respect to L if and only if there exits m ∈ N and an invariant section s : X → L such that s(x) 6= 0. Let X(L) denote the set of semistable points in X , then there is a projective variety X(L)//G and a G-invariant surjective algebraic map π : X(L) → X(L)//G such that
منابع مشابه
Transversality theory, cobordisms, and invariants of symplectic quotients
This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients that we consider are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic manifold by a compact torus. A companion paper [23] examines symplectic quotients by a nonabelian group, showing how to reduce to the maximal torus. Through...
متن کاملTorsion in the Full Orbifold K-theory of Abelian Symplectic Quotients
Let (M,ω,Φ) be a Hamiltonian T -space and let H ⊆ T be a closed Lie subtorus. Under some technical hypotheses on the moment map Φ, we prove that there is no additive torsion in the integral full orbifoldK-theory of the orbifold symplectic quotient [M//H ]. Our main technical tool is an extension to the case of moment map level sets the well-known result that components of the moment map of a Ha...
متن کاملOn Fibers of Algebraic Invariant Moment Maps
In this paper we study some properties of fibers of the invariant moment map for a Hamiltonian action of a reductive group on an affine symplectic variety. We prove that all fibers have equal dimension. Further, under some additional restrictions, we show that the quotients of fibers are irreducible normal schemes.
متن کاملComplete Invariants for Hamiltonian Torus Actions with Two Dimensional Quotients
We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces.
متن کاملOn the $k$-ary Moment Map
The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.
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 2008