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Existence of flips for generalized lc pairs
Christopher D. Hacon,Jihao Liu +1 more
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TLDR
In this article, the existence of flips for NQC generalized lc pairs was proved, and the cone and contraction theorems for generalized Lc pairs were shown to be true.Abstract:
We prove the existence of flips for $\mathbb Q$-factorial NQC generalized lc pairs, and the cone and contraction theorems for NQC generalized lc pairs. This answers a question of C. Birkar which was conjectured by J. Han and Z. Li. As an immediate application, we show that we can run the minimal model program for $\mathbb Q$-factorial NQC generalized lc pairs. In particular, we complete the minimal model program for $\mathbb Q$-factorial NQC generalized lc pairs in dimension $\leq 3$ and pseudo-effective $\mathbb Q$-factorial NQC generalized lc pairs in dimension $4$.read more
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Intersection theory of nef b-divisor classes
Nguyen-Bac Dang,Charles Favre +1 more
TL;DR: In this article, it was shown that any b-divisor class on a projective variety is a decreasing limit of Cartier classes, and that any big and basepoint free curve class is a power of a b-Divisor.
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Special MMP for log canonical generalised pairs
TL;DR: In this article, it was shown that minimal models of NQC log canonical generalised pairs with smooth models of smooth varieties exist, assuming the existence of minimal models for smooth varieties.
References
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Book
Birational Geometry of Algebraic Varieties
János Kollár,Shigefumi Mori +1 more
TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
Journal ArticleDOI
Existence of minimal models for varieties of log general type
TL;DR: In this paper, it was shown that pl-flips exist in dimension n − 1, assuming finite generation in dimension N − 1 and assuming that pl flips exist in all dimensions.
Proceedings ArticleDOI
Introduction to the Minimal Model Problem
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