Related papers: Effective base point free theorem for log canonica…

We prove Koll\'ar-type effective basepoint-free theorems for quasi-log canonical pairs.

We prove Angehrn-Siu type effective base point freeness and point separation for log canonical pairs.

We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…

We prove a base point free theorem for nef and log big divisors on log canonical surfaces.

We prove the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field.

We prove the Angehrn-Siu Type effective freeness and effective point separation for quasi-log canonical pairs. As a natural consequence, we obtain that these two results hold for semi-log canonical pairs. One of the main ingredients of our…

We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Koll\'ar's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone…

We reformulate base point free theorems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the base point free theorem in Fukuda's paper: On numerically…

This paper proposes a Fujita-type freeness conjecture for semi-log canonical pairs. We prove it for curves and surfaces by using the theory of quasi-log schemes and give some effective very ampleness results for stable surfaces and semi-log…

We prove the base point free theorem for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. Moreover, we show abundance in the case of numerically trivial log canonical foliated pairs of rank one in any…

We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.

We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.

We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log…

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

We prove the existence of log canonical modifications for a log pair. As an application, together with Koll\"ar's gluing theory, we remove the assumption in the first named author's work [Odaka11], which shows that K-semistable polarized…

Let $(X,\Delta)$ be a proper dlt pair and $L$ a nef Cartier divisor such that $aL-(K_X+\Delta)$ is nef and log big on $(X,\Delta)$ for some $a\in {\mathbb Z}_{>0}$. Then $|mL|$ is base point free for every $m\gg 0$.

We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We prove the Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs. We also give a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.

This paper is a gentle introduction to the theory of quasi-log varieties by Ambro. We explain the fundamental theorems for the log minimal model program for log canonical pairs. More precisely, we give a proof of the base point free theorem…