相关论文: Toric Rigid Spaces

Here it is shown how to combine two generically globally rigid bar frameworks in $d$-space to get another generically globally rigid framework. The construction is to identify $d+1$ vertices from each of the frameworks and erase one of the…

We survey some results on toric topology.

We introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its…

In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…

We associate a geometric space to an arbitrary convex polytope. Our construction parallels the construction by D. Cox of a toric variety as a GIT quotient. The spaces that we obtain are endowed with a natural stratification and perfectly…

In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also…

In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.

This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems

In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…

In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.

In this paper, we introduce round and sleek topological spaces and study their properties.

Several rigidity problems in toric topology are addressed in \cite{ma-su08}. In this paper, we survey results on those problems including recent development.

In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction…

In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

Using toric geometry we prove a B\'ezout type theorem for weighted projective spaces.

Given any countable group $G$, we construct uncountably many quasi-isometry classes of proper geodesic metric spaces with quasi-isometry group isomorphic to $G$. Moreover, if the group $G$ is a hyperbolic group, the spaces we construct are…

This note describes how to construct toroidal polyhedra which are homotopic to a given type of knot and which admit an isohedral tiling of 3-space.

Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of…