10 citations · 34 across the 26 of their papers we have counts for
26 papers
Fujiki Class Varieties and a Kähler Criterion
Christopher Hacon, Yi Li, Lingyao Xie
In this article, we show that flips and divisorial contractions preserve the Kähler condition (for strongly -factorial compact Kähler generalized klt pairs with …
On the Kähler MMP and the transcendental base-point-free theorem
Christopher Hacon, Lingyao Xie
In this article, we establish the minimal model program for big gklt Kähler pairs, and in particular we prove Tosatti's transcendental base-point-free conjecture.
Variation of algebraically integrable adjoint foliated structures
Paolo Cascini, Jihao Liu, Fanjun Meng +2
Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with resp…
The extension of numerically trivial divisors on a family
Lingyao Xie
Let be a projective morphism of normal varieties. Assume is an open subset of and is a -divisor on such that …
On finite generation and boundedness of adjoint foliated structures
Paolo Cascini, Jingjun Han, Jihao Liu +4
We prove the existence of good minimal models for any klt algebraically integrable adjoint foliated structure of general type, and that Fano algebraically integrable adjoint foliat…
Boundedness of complements for generalized pairs
Guodu Chen, Jingjun Han, Yang He +1
We prove the boundedness of complements for Fano type generalized pairs (with the boundary coefficient set ) after Shokurov.
A generalized non-vanishing theorem on surfaces
Jihao Liu, Lingyao Xie
We show that the anti-canonical bundle of any -factorial surface is numerically effective if and only if it is pseudo-effective. To prove this, we establish a numerical…
Minimal model program for algebraically integrable adjoint foliated structures
Paolo Cascini, Jingjun Han, Jihao Liu +4
For -factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we de…
Minimal model program for algebraically integrable foliations on klt varieties
Jihao Liu, Fanjun Meng, Lingyao Xie
For lc algebraically integrable foliations on klt varieties, we prove the base-point-freeness theorem, the contraction theorem, and the existence of flips. The first result resolve…
Minimal model program for algebraically integrable foliations and generalized pairs
Guodu Chen, Jingjun Han, Jihao Liu +1
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 min…
Uniform rational polytopes of foliated threefolds and the global ACC
Jihao Liu, Fanjun Meng, Lingyao Xie
In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension . As an application, we prove the global ACC fo…
Vanishing theorems for generalized pairs
Bingyi Chen, Jihao Liu, Lingyao Xie
We establish the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As a consequence, we provide a new proof of the base-point-freeness…
Complements, index theorem, and minimal log discrepancies of foliated surface singularities
Jihao Liu, Fanjun Meng, Lingyao Xie
We present an extension of several results on pairs and varieties to foliated surface pairs. We prove the boundedness of local complements, the local index theorem, and the uniform…
ACC for generalized log canonical thresholds for complex analytic spaces
Christopher Hacon, Lingyao Xie
We show that generalized log canonical thresholds for complex analytic spaces satisfy the ACC and we characterize the accumulation points.
Remarks on the existence of minimal models of log canonical generalized pairs
Nikolaos Tsakanikas, Lingyao Xie
Given an NQC log canonical generalized pair whose underlying variety is not necessarily -factorial, we show that one may run a -MMP with scalin…
Contraction theorem for generalized pairs
Lingyao Xie
We use Kollár'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.
Semi-ampleness of NQC generalized log canonical pairs
Jihao Liu, Lingyao Xie
We establish a Kollár-type gluing theory for NQC generalized log canonical pairs and use it to prove semi-ampleness results of NQC generalized pairs. As consequences, we prove the…
Infinitesimal structure of log canonical thresholds
Jihao Liu, Fanjun Meng, Lingyao Xie
We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension accumulates…
Relative Nakayama-Zariski decomposition and minimal models of generalized pairs
Jihao Liu, Lingyao Xie
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 M…
On generalized lc pairs with -log abundant nef part
Junpeng Jiao, Jihao Liu, Lingyao Xie
We study the behavior of generalized lc pairs with -log abundant nef part, a meticulously designed structure on algebraic varieties. We show that this structure…
On the fixed part of pluricanonical systems for surfaces
Jihao Liu, Lingyao Xie
We show that defines a birational map and has no fixed part for some bounded positive integer for any -lc surface such that is big and nef. For…
On the existence of flips for threefolds in mixed characteristic
Lingyao Xie, Qingyuan Xue
We provide a detailed proof of the validity of the Minimal Model Program for threefolds over excellent Dedekind separated schemes whose residue fields do not have characteristic 2…
On the termination of the MMP for semi-stable fourfolds in mixed characteristic
Lingyao Xie, Qingyuan Xue
We improve on the result of Hacon and Witaszek by showing that the MMP for semi-stable fourfolds in mixed characteristic terminates in several new situations. In particular, we sho…
Rational nef and anti-nef polytopes are not uniform
Lingyao Xie
We give two examples which show that rational nef and anti-nef polytopes are not uniform even for klt surface pairs, answering a question of Chen-Han. We also show that rational ne…