Related papers: Singularities and K-semistability
We introduce $\mathfrak{f}$-stability, a modification of fibration stability of Dervan-Sektnan [12], and show that $\mathfrak{f}$-semistable fibrations have only semi log canonical singularities. Moreover, $\mathfrak{f}$-stability puts…
The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice…
We compute the genus-0 permutation-equivariant quantum K-theory of Fermat singularities, in parallel with the Givental-Lee theory for projective varieties. We extend Givental-Tonita's formalism of adelic Lagrangian cones to the singularity…
We formulate a notion of K-stability for K\"ahler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies…
The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-th order regularization designed to balance bulk and…
In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.
The aim of this paper is to present an extension theorem for the functions separately holomorphic on generalized (N,k)-crosses with pluripolar singularities.
The purpose of the present paper is to set up a formalism inspired from non-Archimedean geometry to study K-stability. We first provide a detailed analysis of Duistermaat-Heckman measures in the context of test configurations,…
We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i…
We study "polync varieties", whose singularities are locally products of normal crossing (nc) singularities. We introduce the notion of d-semistability of such varieties, and generalize work of Friedman and Kawamata-Namikawa to address the…
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
We study in this paper real-valued functions on the space of all sub-$\sigma$-algebras of a probability measure space, and introduce the notion of Kudo-continuity, which is an a priori strengthening of continuity with respect to strong…
Let K be an abstract elementary class satisfying the joint embedding and the amalgamation properties. Let m be a cardinal above the the L\"owenheim-Skolem number of the class. Suppose K satisfies the disjoint amalgamation property for limit…
Let $f$ be a function in the Eremenko-Lyubich class $\mathcal{B}$, and let $U$ be an unbounded, forward invariant Fatou component of $f$. We relate the number of singularities of an inner function associated to $f|_U$ with the number of…
If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K…
For a normal F-finite variety $X$ and a boundary divisor $\Delta$ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair $(X,\Delta)$.…
Over the past couple of years we have had significant progress in determining long-distance singularities in gauge-theory scattering amplitudes of massless particles beyond the planar limit. Upon considering all kinematic invariants much…
Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function $K_{i\tau}(x)$. The results can be applied, for instance, to study the summability of the divergent…
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation…
We provide an alternative definition for the familiar concept of regular singularity for meromorphic connections. Our new formulation does not use derived categories, and it also avoids the necessity of finding a special good filtration as…