Related papers: K-stability and polystable degenerations of polari…
We study the question for which commutative ring spectra $A$ the tensor of a simplicial set $X$ with $A$, $X \otimes A$, is a stable invariant in the sense that it depends only on the homotopy type of $\Sigma X$. We prove several structural…
For a trivial elliptic fibration $X=C \times S$ with $C$ an elliptic curve and $S$ a projective K3 surface of Picard rank $1$, we study how various notions of stability behave under the Fourier-Mukai autoequivalence $\Phi$ on $D^b(X)$,…
In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we…
In a form which include the mother compound, we studied the extended Hubbard-type model with the orbital degeneracy for any doping concentration. Meanfield phase diagram and the spin wave excitation in RPA are calculated. It turned out that…
We prove that all smooth Fano threefolds with Picard rank 2 and degree 28 are K-polystable, except for some explicit cases which we describe. We also give a classification of the normal bundle of a rational normal quartic curve in a smooth…
On a K-unstable toric variety we show the existence of an optimal destabilising convex function. We show that if this is piecewise linear then it gives rise to a decomposition into semistable pieces analogous to the Harder-Narasimhan…
The holomorphic invariants introduced by Futaki as obstruction to the asymptotic Chow semistability are studied by an algebraic-geometric point of view and are shown to be the Mumford weights of suitable line bundles on the Hilbert scheme.…
A monomial self-map $f$ on a complex toric variety is said to be $k$-stable if the action induced on the $2k$-cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of…
We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results of existence of Kahler-Einstein metrics with cone…
We prove singularity criteria for the $t$-K-stability of adjoint foliated structures. We first show that K-semistability of adjoint foliated structures implies log canonicity by extending Odaka's flag ideal characterisation of the mixed…
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{\"o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the…
We propose an operational degree of polarization in terms of the variance of the projected Stokes vector minimized over all the directions of the Poincar\'e sphere. We examine the properties of this degree and show that some problems…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
Complete determination of the polarisation state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number $\kappa$ of the…
The first secant variety $\Sigma$ of a rational normal curve of degree $d \geq 3$ is known to be a $\mathbf{Q}$-Fano threefold. In this paper, we prove that $\Sigma$ is K-polystable, and hence, $\Sigma$ admits a weak K\"{a}hler-Einstein…
We study in Kaluza-Klein theories stability of the extra space against "squashing", in other words, the homogeneous deformation. Quantum fluctuations of matter fields at one-loop level are taken into consideration. We calculate the…
We study the problem of the existence and the holomorphicity of the Monge-Amp\`ere foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Amp\`ere equation even at points of arbitrary degeneracy. We obtain…
Given a klt singularity $x\in (X, D)$, we show that a quasi-monomial valuation $v$ with a finitely generated associated graded ring is the minimizer of the normalized volume function $\widehat{\rm vol}_{(X,D),x}$, if and only if $v$ induces…
It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan construct a canonical filtration of the section ring, called Loewy filtration, and conjecture that the Loewy filtration destabilizes…
Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds…