Jingjun Han

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.

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…

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.

math.AG2026

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…

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…

cs.LG2025

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)…

Boundedness of complements for log Calabi-Yau threefolds

Guodu Chen, Jingjun Han, Qingyuan Xue

In this paper, we study the theory of complements, introduced by Shokurov, for Calabi-Yau type varieties with the coefficient set $[0, 1]$ . We show that there exists a finite set of…

cs.SC2014

Constructing Fewer Open Cells by GCD Computation in CAD Projection

Jingjun Han, Liyun Dai, Bican Xia

A new projection operator based on cylindrical algebraic decomposition (CAD) is proposed. The new operator computes the intersection of projection factor sets produced by different…

On termination of flips and exceptionally non-canonical singularities

Jingjun Han, Jihao Liu

We systematically introduce and study a new type of singularities, namely, exceptionally non-canonical (enc) singularities. This class of singularities plays an important role in t…

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.

ACC for minimal log discrepancies of terminal threefolds

Jingjun Han, Jihao Liu, Yujie Luo

We prove that the ACC conjecture for minimal log discrepancies holds for threefolds in $[1 - I^´, + \infty)$ , where $I^´ > 0$ only depends on the coefficient set. We also study Reid's gene…

ACC for minimal log discrepancies of exceptional singularities

Jingjun Han, Jihao Liu, V. V. Shokurov

We prove the existence of $n$ -complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, w…

math.AG2017

On Fujita's conjecture for pseudo-effective thresholds

Jingjun Han, Zhan Li

We show Fujita's spectrum conjecture for $I^µ$ -log canonical pairs and Fujita's log spectrum conjecture for log canonical pairs. Then, we generalize the pseudo-effective threshold o…

math.AG2023

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…

On a generalized canonical bundle formula for generically finite morphisms

Jingjun Han, Wenfei Liu

We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with $R$ -coefficients). This complements Filipazzi's canonical bu…

math.AG2019

Weak Zariski decompositions and log terminal models for generalized polarized pairs

Jingjun Han, Zhan Li

We show that the existence of a birational weak Zariski decomposition for a pseudo-effective generalized polarized lc pair is equivalent to the existence of a generalized polarized…

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 $5$ , and give explicit bounds (in terms of topological invariants and volume of divisors) on the number…

math.GM2016

Multivariate discriminant and iterated resultant

Jingjun Han

In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form $f (X_{n})$ with even degree $d$ , if the polynomial i…

math.AG2021

Shokurov's conjecture on conic bundles with canonical singularities

Jingjun Han, Chen Jiang, Yujie Luo

A conic bundle is a contraction $X \to Z$ between normal varieties of relative dimension $1$ such that $- K_{X}$ is relatively ample. We prove a conjecture of Shokurov which predicts t…

On accumulation points of pseudo-effective thresholds

Jingjun Han, Zhan Li

We characterize a $k$ -th accumulation point of pseudo-effective thresholds of $n$ -dimensional varieties as certain invariant associates to a numerically trivial pair of an $(n - k)$ -…

cs.LO2012

A Simple Quantifier-free Formula of Positive Semidefinite Cyclic Ternary Quartic Forms

Jingjun Han

Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, functi…

On numerical nonvanishing for generalized log canonical pairs

Jingjun Han, Wenfei Liu

The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing co…

math.AG2023

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…

Birational boundedness of rationally connected Calabi-Yau 3-folds

Weichung Chen, Gabriele Di Cerbo, Jingjun Han +2

We prove that rationally connected Calabi--Yau 3-folds with kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected $3…

math.AG2018

On a connectedness principle of Shokurov-KollÃ¡r type

Christopher D. Hacon, Jingjun Han

Let $(X, I^)$ be a log pair over $S$ , such that $- (K_{X} + I^)$ is nef over $S$ . It is conjectured that the intersection of the non-klt (non Kawamata log terminal) locus of $(X, I^)$ wit…

Uniform rational polytopes for Iitaka dimensions

Guodu Chen, Jingjun Han, Jihao Liu

In this paper, we continue to develop the theories on functional pairs and uniform rational polytopes. We show that there is a uniform perturbation for Iitaka dimensions of pseudo-…

cs.SC2019

Open Weak CAD and its Applications

Jingjun Han, Liyun Dai, Hoon Hong +1

The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing project…

math.AG2019

Bounded deformations of $(I^µ, I^´)$ -log canonical singularities

Jingjun Han, Jihao Liu, JoaquÃn Moraga

In this paper we study $(I^µ, I^´)$ -lc singularites, i.e. $I^µ$ -lc singularities admitting a $I^´$ -plt blow-up. We prove that $n$ -dimensional $(I^µ, I^´)$ -lc singularities are bounded up t…

Boundedness of $(I^µ, n)$ -Complements for Surfaces

Guodu Chen, Jingjun Han

We show the existence of $(I^µ, n)$ -complements for $(I^µ, R)$ -complementary surface pairs when the coefficients of boundaries belong to a DCC set.

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…

ACC for local volumes and boundedness of singularities

Jingjun Han, Yuchen Liu, Lu Qi

The ACC conjecture for local volumes predicts that the set of local volumes of klt singularities $x \in (X, I^)$ satisfies the ACC if the coefficients of $I^$ belong to a DCC set. In…

ACC for log canonical threshold polytopes

Jingjun Han, Zhan Li, Lu Qi

We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition.

On boundedness of divisors computing minimal log discrepancies for surfaces

Jingjun Han, Yujie Luo

Let $I^$ be a finite set, and $X ∋ x$ a fixed klt germ. For any lc germ $(X ∋ x, B := \sum_{i} b_{i} B_{i})$ such that $b_{i} \in I^$ , Nakamura's conjecture, which is equivalent to the ACC…

Birational boundedness of rationally connected log Calabi-Yau pairs with fixed index

Jingjun Han, Chen Jiang

We show that the set of rationally connected projective varieties $X$ of a fixed dimension such that $(X, B)$ is klt, and $- l (K_{X} + B)$ is Cartier and nef for some fixed positive inte…

Effective birationality for sub-pairs with real coefficients

Jingjun Han, Jihao Liu

For $I^µ$ -lc Fano type varieties $X$ of dimension $d$ and a given finite set $I^$ , we show that there exists a positive integer $m_{0}$ which only depends on $I^µ, d$ and $I^$ , such tha…

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 $[0, 1]$ ) after Shokurov.

Minimal model program for algebraically integrable adjoint foliated structures

Paolo Cascini, Jingjun Han, Jihao Liu +4

For $Q$ -factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we de…

cs.SC2013

Proving Inequalities and Solving Global Optimization Problems via Simplified CAD Projection

Jingjun Han, Zhi Jin, Bican Xia

Let $\xx_n=(x_1,\ldots,x_n)$ and $f\in \R[\xx_n,k]$. The problem of finding all $k_{0}$ such that $f(\xx_n,k_0)\ge 0$ on $R^{n}$ is considered in this paper, which obviously t…