Related papers: K stability and stability of chiral ring
In this paper we study the relative Chow and $K$-stability of toric manifolds in the toric sense. First, we give a criterion for relative $K$-stability and instability of toric Fano manifolds in the toric sense. The reduction of relative…
We introduce an inductive argument for proving birational superrigidity and K-stability of singular Fano complete intersections of index one, using the same types of information from lower dimensions. In particular, we prove that a…
In multidimensional gravity with an arbitrary number of internal Ricci-flat factor spaces, interacting with electric and magnetic $p$-branes, spherically symmetric configurations are considered. It is shown that all single-brane black-hole…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
The category of quasi frames (or qframes) is introduced and studied. In the context of qframes we can jointly study problems related to the L-Surjunctivity and Stable Finiteness Conjectures. As a consequences of our main results, we can…
Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. Firstly, K field theories allow for soliton solutions…
For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of…
We consider the Principal Chiral Field model posed in 1+1 dimensions into the Lie group $\text{SL}(2,\mathbb R)$. In this work we show the nonlinear stability of small enough nonsingular solitons. The method of proof involves the use of…
After a short review of the algebraic setting of N=2 superconformal field theories, their chiral ring and their perturbations, I present some recent results on curious relations between the integrability of their perturbations and algebraic…
We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with…
K-theory provides a framework for classifying Ramond-Ramond (RR) charges and fields. K-theory of manifolds has a natural extension to K-theory of noncommutative algebras, such as the algebra considered in noncommutative Yang-Mills theory or…
Let $X$ be a nonsingular complex projective toric variety. We address the question of semi-stability as well as stability for the tangent bundle $T{X}$. In particular, a complete answer is given when $X$ is a Fano toric variety of dimension…
In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of interest fit into this framework, in particular algebraic- and…
The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wave length physics of the system is precisely the supersymmetric nonlinear sigma-model for quasi…
We consider the quintic nonlinear Schr{\"o}dinger on the circle. By applying a Birkhoff procedure and a KAM theorem, we exihibit a three dimension invariant torus that is linearly unstable. In comparison, we also prove that two dimensional…
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…
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account…
Spontaneous chiral symmetry breaking in three dimensional ($d=3$) quantum electrodynamics is understood as annihilation of an infrared-stable fixed point that describes the large-N conformal phase by another unstable fixed point at a…
In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…
We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite…