Related papers: ACC for log canonical thresholds for complex analy…

We show that every limit of log canonical thresholds of n-variable functions is also a log canonical threshold of an (n-1)-variable function.

As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…

We prove Koll\'ar's effective base point free theorem for log canonical pairs.

We show that the family of semi log canonical pairs with ample log canonical class and with fixed volume is bounded.

We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…

We prove that a Kawamata log terminal pair has the canonical model.

The special case of closed subsets of C^n is briefly discussed.

A necessary and sufficient compactness criterion in Schauder Spaces is proved.

A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with…

This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…

We define the "source" and the "spring" of a log canonical center and use them to solve several problems in higher-codimension adjunction. The main application is to the construction of semi log canonical pairs. Version 2: References…

We prove that for each positive integer $n$ there exists a positive number $\epsilon_n$ so that $n$-dimensional toric quotient singularities satisfy the ACC for mld's on the interval $(0,\epsilon_n)$. In the course of the proof, we will…

We compute global log canonical thresholds, or equivalently alpha invariants, of birationally rigid orbifold Fano threefolds embedded in weighted projective spaces as codimension two or three. As an important application, we prove that most…

We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…

For a locally defined real analytic function, we study the relation between the oscillation index of oscillatory integrals and the real log canonical threshold. The former is always negative, and its absolute value is greater than or equal…

Let X be a smooth variety over a field of positive characteristic, and let E be an overconvergent isocrystal on X. We establish a criterion for the existence of a "canonical logarithmic extension" of E to a good compactification of X. In…

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa's conjecture on exponential sums, with the log-canonical threshold in the…

In this paper, we investigate the multiplicities and the log canonical thresholds of abelian quotient complete intersection singularities in term of the special datum. Moreover we give bounds of the multiplicity of abelian quotient complete…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…