12 papers
A Sharp inequality between local volumes and minimal log discrepancies
Jingjun Han
We answer a question of Li--Liu--Xu: every -dimensional klt germ , where , satisfies the sharp inequality \[ \widehat{\operatorname{vol}}(x,X,Δ)\le n^{n-1}\ope…
Max It or Miss It: Benchmarking LLM On Solving Extremal Problems
Binxin Gao, Jingjun Han
Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT)…
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…
Boundedness in general type MMP
Jingjun Han, Lu Qi, Ziquan Zhuang
We show that in any sequence of a general type MMP, the minimal log discrepancy of singularities takes at most finitely many values, and the fibers of all the extremal contractions…
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…
Total Cartier index of a bounded family
Jingjun Han, Chen Jiang
We prove that the total Cartier index of a bounded family of projective varieties of klt type is bounded.
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.
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.
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…