Related papers: The locus of log canonical singularities
We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.
A plurisubharmonic weight is log canonical if it is at the critical point of turning non-integrable. Given a log canonical plurisubharmonic weight, we show that locally there always exists a log canonical `holomorphic' weight having the…
Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical…
We prove the normality of minimal log canonical centers on threefold pairs which residue fields are perfect of residue characteristics $p\neq 2,3 $ and $5$. We also show that the union of all log canonical centers on threefold pairs with…
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…
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 propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.
We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.
We give a method to investigate isolated log canonical singularities with index one which are not log terminal. Our method depends on the minimal model program. One of the main purposes is to prove that our invariant coincides with Ishii's…
We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.
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.
A recurring difficulty in the Minimal Model Program is that while log terminal singularities are quite well behaved (for instance, they are rational), log canonical singularities are much more complicated; they need not even be…
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 show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
We define a class of singularity on arbitrary pairs of a normal variety and an effective $\mathbb{R}$-divisor on it, which we call pseudo-lc in this paper. This is a generalization of the usual lc singularity of pairs and log canonical…
Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also…
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…
We introduce the notion of quasi-log complex analytic spaces and establish various fundamental properties. Moreover, we prove that a semi-log canonical pair naturally has a quasi-log complex analytic space structure. This paper is part of…
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 show that some properties of log canonical centers of a log canonical pair (X,D) also hold for certain subvarieties that are close to being a log canonical center. As a consequence, we obtain that if one works with deformations of pairs…