Related papers: Minimal log discrepancies in positive characterist…

1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable curves. Each stable pair has semi log canonical…

We classify two-dimensional toric log germs in terms of their minimal log discrepancy.

A Mukai variety is a Fano n-fold of index n-2. In this paper we study the fundamental divisor of a Mukai variety with at worst log terminal singularities. The main result is a complete classification of log terminal Mukai varieties which…

We show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous.

We show that there exists a positive real number $\delta>0$ such that for any normal quasi-projective $\mathbb{Q}$-Gorenstein $3$-fold $X$, if $X$ has worse than canonical singularities, that is, the minimal log discrepancy of $X$ is less…

In this paper, we prove the termination of 4-fold semi-stable log flips under the assumption that there always exist 4-fold (semi-stable) log flips.

Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these…

We prove the existence of $n$-complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, we develop the theory of complements for real coefficients.…

We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the sequence is log-convex and show that this holds eventually for…

Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants have nice…

The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some…

We prove that the moduli b-divisor of an lc-trivial fibration from a log canonical pair is log abundant. The result follows from a theorem on the restriction of the moduli b-divisor, based on a theory of lc-trivial morphisms, which allows…

Given a singular curve on a smooth surface, we determine which exceptional divisors on the minimal resolution of that curve contribute toward its jumping numbers.

Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…

The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…

In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…

We introduce an approach of Riemann--Roch theorem to the boundedness problem of minimal log discrepancies in fixed dimension. After reducing it to the case of a Gorenstein terminal singularity, firstly we prove that its minimal log…

We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical $4$-folds.

We prove that a positive proportion of the gaps between consecutive primes are short gaps of length less than any fixed fraction of the average spacing between primes.

We prove the abundance theorem for numerically trivial log canonical divisors of log canonical pairs and semi-log canonical pairs.