Related papers: Torus equivariant K-stability
A C*-algebra is said to be K-stable if its nonstable K-groups are naturally isomorphic to the usual K-theory groups. We study continuous $C(X)$-algebras, each of whose fibers are K-stable. We show that such an algebra is itself K-stable…
A monomial (or equivariant) selfmap of a toric variety is called stable if its action on the Picard group commutes with iteration. Generalizing work of Favre to higher dimensions, we show that under suitable conditions, a monomial map can…
Let $X$ be a torus manifold with locally standard action of a compact torus $T$ of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds.…
We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.
We obtain a generalization of the Kodaira-Morrow stability theorem for cosymplectic structures. We investigate cosymplectic geometry on Lie groups and on their compact quotients by uniform discrete subgroups. In this way we show that a…
We show that certain isomorphisms of (twisted) KR-groups that underlie T-dualities of torus orientifold string theories have purely algebraic analogues in terms of algebraic K-theory of real varieties and equivalences of derived categories…
We formulate an effective variant of the Yau-Tian-Donaldson conjecture, then review effective results on K-stability of spherical varieties, that is, K-stability criterions which can be effectively computed given the combinatorial data…
On a compact connected Lie group $G$, we study the global solvability and the cohomology spaces of the differential complex associated with an essentially real involutive structure that is invariant under left translations. We prove that…
The second author has shown that existence of extremal K\"ahler metrics on semisimple principal toric fibrations is equivalent to a notion of weighted uniform K-stability, read off from the moment polytope. The purpose of this article is to…
Our aim is to bring the theory of analogous polytopes to bear on the study of quasitoric manifolds, in the context of stably complex manifolds with compatible torus action. By way of application, we give an explicit construction of a…
As recently pointed out by Li and Xu, the definition of K-stability, and the author's proof of K-stability for cscK manifolds without holomorphic vector fields, need to be altered slightly: the Donaldson-Futaki invariant is positive for all…
Kaneyama and Klyachko have shown that any torus equivariant vector bundle of rank $r$ over $\mathbb{CP}^n$ splits if $r < n$. In particular, any such bundle is not slope stable. In contrast, we provide explicit examples of stable…
The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…
Given a one parameter flat family of polarized algebraic varieties, we show that any K-stable limit is unique. In particular, moduli spaces of K-stable polarized varieties are automatically Hausdorff when they exist. We also give a…
The Pontryagin-Thom theorem gives an isomorphism from the cobordism group of framed $n$-manifolds to the $n$th stable homotopy group of the sphere spectrum. In this paper, we prove the generalization of the Pontryagin-Thom theorem for…
The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…
The {\it torus manifolds} have been defined and studied by M. Masuda and T. Panov (arXiv:math.AT/0306100) who in particular describe its cohomology ring structure. In this note we shall describe the topological $K$-ring of a class of torus…
We show that if the rotation set of a homeomorphism of the torus is stable under small perturbations of the dynamics, then it is a convex polygon with rational vertices. We also show that such homeomorphisms are $C^0$-generic and have…
Let $T$ be a compact torus. We prove that, up to equivariant rational equivalence, the category of $T$-simply connected, $T$-finite type $T$-spaces with finitely many isotropy types is completely described by certain finite systems of…
We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical…