相关论文: Torus Actions on Quotients of Affine Spaces

We study the restrictions, the strict fixed points, and the strict quotients of the partition complex $|\Pi_n|$, which is the $\Sigma_n$-space attached to the poset of proper nontrivial partitions of the set $\{1,\ldots,n\}$. We express the…

We consider actions of real Lie subgroups G of complex reductive Lie groups on Kaehlerian spaces. Our main result is the openness of the set of semistable points with respect to a momentum map and the action of G.

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

In this paper we study actions of reductive groups on affine spaces. We prove that there is a fan structure on the space of characters of the group, which parameterizes the possible invariant quotients. In the second half of the paper we…

Let $(X, T^{1,0}X)$ be a connected orientable compact CR manifold of dimension $2n+1$, $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplitz operators on $X$ and we establish star product for some…

We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds etale locally and we provide some evidence for this conjecture.…

We present an algorithm to compute the GIT-fan of algebraic torus actions on affine varieties.

This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants,…

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…

Let $G$ be a complex semisimple algebraic group and $X$ be a complex symmetric homogeneous $G$-variety. Assume that both $G$, $X$ as well as the $G$-action on $X$ are defined over real numbers. Then $G(\mathbb{R})$ acts on $X(\mathbb{R})$…

Fix some prime number $\ell$ and consider an open subgroup $G$ either of $\operatorname{GL}_2(\mathbb{Z}_\ell)$ or of the normalizer of a Cartan subgroup of $\operatorname{GL}_2(\mathbb{Z}_\ell)$. The elements of $G$ act on…

We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…

The group action which defines the moduli problem for the deformation space of flat affine structures on the two-torus is the action of the affine group $\Aff(2)$ on $\bbR^2$. Since this action has non-compact stabiliser $\GL(2,\bbR)$, the…

We apply the Guillemin-Lerman-Sternberg theorem to reprove a formula of Heckman for the Duistermaat-Heckman measure associated to the coadjoint action of $T$, a maximal torus of a compact semisimple Lie group $G$, on a regular coadjoint…

A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $p\in X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility…

A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the group of birational automorphisms of a compact complex Kaehler surface. We established in our previous paper the following Tits-type…

For an endomorphism $s:V\rightarrow V$ of a finite dimensional complex vector space and an action of a torus $T$ on the full flag variety $\text{GL}_n({\mathbb C})/B$, we give a description of its fixed point set when $s$ is semisimple or…

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that $G$ is a group for which there is a bound on the orders of its finite subgroups. We prove that if $G$ acts properly on a…

We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…

Let $X$ be a complex toric variety equipped with the action of an algebraic torus $T$, and let $G$ be a complex linear algebraic group. We classify all $T$-equivariant principal $G$-bundles $\mathcal{E}$ over $X$ and the morphisms between…