38 citations · 67 across the 18 of their papers we have counts for
19 papers
Criteria of isolated weighted homogeneous hypersurface singularities using Logarithmic vector fields
Jihao Liu, Xiping Zhang
We prove a conjecture of da Silva Machado and Seade that characterizes weighted homogeneous isolated hypersurface singularities through the existence of a logarithmic vector field…
Existence of the minimal model program for log canonical generalized pairs
Zhengyu Hu, Jihao Liu
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, toge…
Dual complexes of qdlt Fano type models and strong complete regularity
Jihao Liu, Konstantin Loginov
We introduce birational strong complete regularity and strong complete regularity, two numerical invariants for pairs of (relative) Fano type. They are defined using variants of qd…
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…
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 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…
The minimal volume of surfaces of log general type with non-empty non-klt locus
Jihao Liu, Wenfei Liu
We show that the minimal volume of surfaces of log general type, with non-empty non-klt locus on the ample model, is . Furthermore, the ample model achieving the…
ACC for lc thresholds for algebraically integrable foliations
Omprokash Das, Jihao Liu, Roktim Mascharak
We prove the ACC for lc thresholds and the global ACC for algebraically integrable foliations and provide applications.
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…
Optimal bounds on surfaces
Jihao Liu, V. V. Shokurov
We prove that the first gap of -complementary thresholds of surfaces is . More precisely, the largest -complementary threshold for surfaces that…
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…
On global ACC for foliated threefolds
Jihao Liu, Yujie Luo, Fanjun Meng
In this paper, we prove the rational coefficient case of the global ACC for foliated threefolds. Specifically, we consider any lc foliated log Calabi-Yau triple …
On effective log Iitaka fibrations and existence of complements
Guodu Chen, Jingjun Han, Jihao Liu
We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. In one direction, we show that t…
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…
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…
Divisors computing minimal log discrepancies on lc surfaces
Jihao Liu, Lingyao Xie
Let be an lc surface germ. If is klt, we show that there exists a divisor computing the minimal log discrepancy of that is a Kollár component of…
ACC for minimal log discrepancies of exceptional singularities
Jingjun Han, Jihao Liu, V. V. Shokurov
We prove the existence of -complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, w…