12 papers
A klt generalized pair with infinitely generated canonical ring
Jihao Liu, Yanze Wang
We construct a projective klt generalized pair over the complex numbers whose generalized log canonical ring is not finitely generated. The main result of this paper is obtained by…
Twelve common flex lines in a general pencil of cubics
Jihao Liu, Yanze Wang
We prove that a general pencil of plane cubics over has exactly common flex lines. This answers a question of Ciliberto, Miranda, and Roé. The main result of this…
A counterexample to the odd-dimensional rank bound for abelian \texorpdfstring{}{p}-group actions
Jihao Liu, Yanze Wang
We disprove the odd-dimensional extension, conjectured by Moraga and recorded by Kollár and Zhuang, of the rank bound for faithful abelian -group actions on smooth Calabi--Yau v…
Effective termination of general type MMPs in dimension at most five
Jingjun Han, Jihao Liu, Ziquan Zhuang
We prove the effective termination of general type MMPs in dimension at most , and give explicit bounds (in terms of topological invariants and volume of divisors) on the number…
Sarkisov program for algebraically integrable and threefold foliations
Yifei Chen, Jihao Liu, Yanze Wang
By applying the theory of the minimal model program for adjoint foliated structures, we establish the Sarkisov program for algebraically integrable foliations on klt varieties: any…
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…
Classification of threefold enc cDV quotient singularities
Jingjun Han, Jihao Liu
We provide a rough classification of threefold exceptionally non-canonical cDV quotient singularities by studying their combinatorial behavior.
Flop between algebraically integrable foliations on potentially klt varieties
Yifei Chen, Jihao Liu, Yanze Wang
We prove that for any two minimal models of an lc algebraically integrable foliated triple on potentially klt varieties, there exist small birational models that are connected by a…
ACC for local volumes
Jingjun Han, Jihao Liu, Lu Qi
We prove the ACC conjecture for local volumes. Moreover, when the local volume is bounded away from zero, we prove Shokurov's ACC conjecture for minimal log discrepancies.
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…
Volume of algebraically integrable foliations and locally stable families
Jingjun Han, Junpeng Jiao, Mengchu Li +1
In this paper, we study the volume of algebraically integrable foliations and locally stable families. We show that, for any canonical algebraically integrable foliation, its volum…
On the equivalence between the effective adjunction conjectures of Prokhorov-Shokurov and of Li
Jingjun Han, Jihao Liu, Qingyuan Xue
Prokhorov and Shokurov introduced the famous effective adjunction conjecture, also known as the effective base-point-freeness conjecture. This conjecture asserts that the moduli co…