Related papers: K-stability and polystable degenerations of polari…
We prove several boundedness results for log Fano pairs with certain K-stability. In particular, we prove that K-semistable log Fano pairs of Maeda type form a log bounded family. We also compute K-semistable domains for some examples.
We consider a uniform dipolar Fermi gas in two-dimensions (2D) where the dipole moments of fermions are aligned by an orientable external field. We obtain the ground state of the gas in Hartree-Fock approximation and investigate RPA…
Let ${\rm k}$ be an algebraically closed field of characteristic 0 and $G$ a connect, reductive group over it. Let $X$ be a projective $G$-variety of complexity 1. We classify $G$-equivariant normal test configurations of $X$ with integral…
For any log Fano pair with a torus action, we associate a computable invariant to it, such that the pair is (weighted) K-polystable if and only if this invariant is greater than one. As an application, we present examples of Fano varieties…
We provide an endpoint stability result for Scott-Zhang type operators in Besov spaces. For globally continuous piecewise polynomials these are bounded from $H^{3/2}$ into $B^{3/2}_{2,\infty}$; for elementwise polynomials these are bounded…
We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a relation among the Seshadri constants, the alpha-invariant…
We extend the Kuga-Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga-Satake abelian varieties, associated to polarized variations of K3…
We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric $\alpha$-stable process under H\"older regularity conditions for the drift term. We partially recover the…
We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict periodic waves and we also present a characterization for all…
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…
This paper concerns the tilt stability for the minimization of the sum of a twice continuously differentiable matrix-valued function and the Ky-Fan $\kappa$-norm. To achieve this goal, we first provide a sufficient and necessary condition…
Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in computing the quantum connection of cotangent…
Let X be a normal complex projective variety with at worst klt singularities, and L a big line bundle on X. We use valuations to study the log canonical threshold of L, as well as another invariant, the stability threshold. The latter…
The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric $G$-varieties of rank 2 which are Fano. When $G$ is…
In this paper, we investigate the orbital stability problem of peakons for a modified Camassa-Holm equation with both quadratic and cubic nonlinearity. This equation was derived from integrable theory and admits peaked soliton (peakon) and…
This paper establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the…
This survey article is an accompaniment to the 2025 Summer Research Institute in Algebraic Geometry Bootcamp on K-stability and K-moduli. It is aimed at graduate students and intended to provide the necessary background to begin research on…
We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of…