Related papers: Toric Hypersymplectic Quotients

This is a brief review of the main results of our paper arXiv:1101.1759 that contains a complete global treatment of the compactified trigonometric Ruijsenaars-Schneider system by quasi-Hamiltonian reduction. Confirming previous conjectures…

We introduce a construction that simultaneously yields cusped spaces of relatively hyperbolic groups, and spaces quasi-isometric to Teichmueller metrics. We use this to study Dehn-filling-like quotients of various groups, among which…

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions of a system of nonlinear first order elliptic partial differential equations in the ambient symplectic manifold. The symplectic manifold carries a…

We construct an oriented cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties, together with a closed two-form which restricts to the symplectic forms on the ends. As…

Symplectic potentials are presented for a wide class of five dimensional toric Sasaki-Einstein manifolds, including L^{a,b,c} which was recently constructed by Cvetic et al. The spectrum of the scalar Laplacian on L^{a,b,c} is also studied.…

Consider a smooth effective action of a torus $\mathbb{T}^n$ on a connected $C^{\infty}$-manifold $M$ of dimension $m$. Then $n\leq m$. In this work we show that if $n<m$, then there exist a complete vector field $X$ on $M$ such that the…

We prove the LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous. This implies that any…

A product of a K3 surface $S$ and a flat 3-dimensional torus $T^3$ is a manifold with holonomy $SU(2)$. Since $SU(2)$ is a subgroup of $G_2$, $S\times T^3$ carries a torsion-free $G_2$-structure. We assume that $S$ admits an action of…

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be…

The action of a torus group $T$ on a symplectic toric manifold $(M,\omega)$ often extends to an effective action of a (non-abelian) compact Lie group $G$. We may think of $T$ and $G$ as compact Lie subgroups of the symplectomorphism group…

Examples of aspherical closed symplectic 4-manifolds are presented whose Sullivan minimal models are (1,n)-formal for any n, without being formal. They have as cohomology algebra, signature, canonical class, those of a product of a closed…

Let a compact torus $T=T^{n-1}$ act on an orientable smooth compact manifold $X=X^{2n}$ effectively, with nonempty finite set of fixed points, and suppose that stabilizers of all points are connected. If $H^{odd}(X)=0$ and the weights of…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…

A Hamiltonian action of a complex torus on a symplectic complex manifold is said to be {\it multiplicity free} if a general orbit is a lagrangian submanifold. To any multiplicity free Hamiltonian action of a complex torus $T\cong…

This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…

We discuss how the global geometry and topology of manifolds depend on different group actions of their fundamental groups, and in particular, how properties of a non-trivial compact 4-dimensional cobordism $M$ whose interior has a complete…

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special}…

We show that two orientable, four-dimensional folded symplectic toric manifolds are isomorphic provided that their orbit spaces have trivial degree-two integral cohomology and there exists a diffeomorphism of the orbit spaces (as manifolds…