Related papers: Minimal model program for log canonical pairs on c…

We discuss the minimal model program for projective morphisms of complex analytic spaces. Roughly speaking, we show that the results obtained by Birkar--Cascini--Hacon--M\textsuperscript{c}Kernan hold true for projective morphisms between…

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.

We study the termination of minimal model programs for log canonical pairs in the complex analytic setting. By using the termination, we prove a relation between the minimal model theory for projective log canonical pairs and that for log…

Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…

We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…

We study relations between two log minimal models of a fixed lc pair. For any two log minimal models of an lc pair constructed with log MMP, we prove that there are small birational models of the log minimal models which can be connected by…

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

We discuss vanishing theorems for projective morphisms between complex analytics spaces and some related results. They will play a crucial role in the minimal model theory for projective morphisms of complex analytic spaces. Roughly…

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.

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 continue our study of the relation between log minimal models and various types of Zariski decompositions. Let $(X,B)$ be a projective log canonical pair. We will show that $(X,B)$ has a log minimal model if either $K_X+B$ birationally…

Using techniques from the theory of foliations, we establish the cone theorem and the contraction theorem for lc generalized pairs in full generality, and meanwhile develop the minimal model program for $\mathbb Q$-factorial foliated dlt…

We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.

We show that given any two minimal models of a generalized lc pair, there exist small birational models which are connected by a sequence of symmetric flops. We also present some applications.

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 introduce linearly decomposable (LD) generalized pairs, which serve as a workable substitute for rational decompositions in the non-NQC setting. Using LD generalized pairs, together with a refinement of special termination and…

We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical…

We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski decomposition. Moreover, we establish a structure theorem…

Let $f:X\to U$ be a projective morphism of normal varieties and $(X,\Delta)$ a dlt pair. We prove that if there is an open set $U^0\subset U$, such that $(X,\Delta)\times_U U^0$ has a good minimal model over $U^0$ and the images of all the…