Related papers: Nakamaye's theorem on log canonical pairs

Let L be a nef line bundle on a projective scheme X in positive characteristic. We prove that the augmented base locus of L is equal to the union of the irreducible closed subsets V of X such that the restriction of L to V is not big. For a…

We show that the augmented base locus coincides with the exceptional locus (i.e. null locus) for any nef $\mathbb{R}$-Cartier divisor on any scheme projective over a field (of any characteristic). Next we prove a semi-ampleness criterion in…

We prove that the asymptotic base loci of an NQC klt generalized pair with big canonical class are uniruled. We also show that the non-nef locus and the diminished base locus of the adjoint divisor of an NQC log canonical generalized pair…

We establish a transcendental generalization of Nakamaye's theorem to compact complex manifolds when the form is not assumed to be closed. We apply the recent analytic technique developed by Collins--Tosatti to show that the non-Hermitian…

In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of…

In this paper, we use canonical bundle formulas to prove some generalizations of an old theorem of Kawamata on the semiampleness of nef and abundant log canonical divisors. In particular, we show that for klt pairs $(X,B)$ with $K_X+B$…

In this paper we investigate various properties of generalised pairs in families, especially boundedness of several kinds. We show that many statements for usual pairs do not hold for generalised pairs. In particular, we construct an…

In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which…

The main purpose of this paper is to make Nakayama's theorem more accessible. We give a proof of Nakayama's theorem based on the negative definiteness of intersection matrices of exceptional curves. In this paper, we treat Nakayama's…

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…

Given a log canonical pair $(X, \Delta)$, we show that $K_X+\Delta$ is nef assuming there is no non-constant map from the affine line with values in the open strata of the stratification induced by the non-klt locus of $(X, \Delta)$. This…

We prove some basic properties of the relative Nakayama-Zariski decomposition. We apply them to the study of lc generalized pairs. We prove the existence of log minimal models or Mori fiber spaces for (relative) lc generalized pairs…

Motivated by Shokurov's ACC Conjecture for log canonical thresholds, we propose an inductive point of view on singularities of pairs, in the case when the ambient variety is smooth. Our main result characterizes the log canonicity of a pair…

We discuss the cone theorem for quasi-log schemes and the Mori hyperbolicity. In particular, we establish that the log canonical divisor of a Mori hyperbolic projective normal pair is nef if it is nef when restricted to the non-lc locus.…

This paper shows that Mustata-Nakamura's conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition…

We extend to normal projective varieties defined over an arbitrary algebraically closed field a result of Ein, Lazarsfeld, Musta\c{t}\u{a}, Nakamaye and Popa characterizing the augmented base locus (aka non-ample locus) of a line bundle on…

Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\Q$-divisor, and that there is a surjective morphism $f\colon X\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\sim_\Q f^*M$ for some $\Q$-divisor $M$, and the augmented…

We apply the theory of the Chow-Mumford line bundle as developed by Arezzo-et-al and build on earlier key insights of Paul and Tian (see \cite{Arezzo:DellaVedova:LaNave} and the references therein). In particular, we give an explicit…

We prove a logarithmic base change theorem for pushforwards of pluri-canonical bundles and use it to deduce that positivity properties of log canonical divisors descend via smooth projective morphisms. As an application, for a surjective…

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…