Related papers: Basic properties of log canonical centers

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is $\ge 1$, and equality holds if and only if the base locus has divisorial components. Consequently the same assertions…

Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite…

We present an explicit formula for the canonical height of a projective toric variety.

We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.

Local log-regular rings are a certain class of Cohen-Macaulay local rings that are treated in logarithmic geometry. Our paper aims to provide purely commutative ring theoretic proof of some ring-theoretic properties of local log-regular…

In characteristic zero, quotient singularities are log terminal. Moreover, we can check whether a quotient variety is canonical or not by using only the age of each element of the relevant finite group if the group does not have…

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

We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.

We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.

The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.

Noncommutative surfaces finite over their centres can be realised as orders over surfaces. The aim of this paper is to present a noncommutative generalisation of rational singularities, which we call numerical rationality, for such orders.…

We prove that the anti-canonical divisors of weak Fano 3-folds with log canonical singularities are semiample. Moreover, we consider semiampleness of the anti-log canonical divisor of any weak log Fano pair with log canonical singularities.…

We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact…

We prove the existence of pl-flips.

We consider minimal compactifications of the complex affine plane. Minimal compactifications of the affine plane with at most log canonical singularities are classified. Moreover, every minimal compactification of the affine plane with at…

Given a three-dimensional projective log canonical pair over a perfect field of characteristic larger than five, there exists a minimal model program that terminates after finitely many steps.

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of rank one local systems on a normal variety are related to the jump loci of a…

For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.

In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain $p$-adic theta relations which are satisfied by the canonical theta…

Given a graded sequence of ideals (a_m) on a smooth variety $X$ having finite log canonical threshold, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log…