25 papers
Disproof of the Yau--Tian--Donaldson conjecture
Jihao Liu
We construct a polarized smooth projective fivefold and prove that it is K-polystable but does not admit a constant scalar curvature Kähler metric. This disproves the Yau--Tian--Do…
Mori dream Jacobian elliptic surfaces of Kodaira dimension one
Antonio Laface, Sichen Li, Jihao Liu
Let be a Jacobian elliptic surface over , and set , so that . Assume that the Mordell--Weil group of is fini…
The equality case of Ehrhart's volume conjecture
Jihao Liu
We prove that every full-dimensional compact convex body in whose barycenter is its unique interior lattice point and whose volume is is a unimodular ima…
A slope-unstable bundle on a surface with 1-homogeneous projectivization
Jihao Liu
We answer affirmatively a question of Fulger and Langer on the interplay between slope semistability and positivity for projective bundles with vanishing discriminant. The main res…
Removing the Torsion-free Hypothesis in a Positivity Theorem on Deligne-Mumford Stacks
Shengyu Hou, Jihao Liu
We remove the torsion-free hypothesis from a positivity theorem of Casalaina-Martin and Zhjeqi, answering a question of them. The main result of this paper was obtained using gener…
Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Jihao Liu, Guoxiong Gao, Zeming Sun +8
Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, sca…
On two questions of Qi on saturated filtrations
Jihao Liu, Haofeng Zhang
We answer two questions of Qi [J. Reine Angew. Math. 830 (2026)] on the metric space of saturated filtrations, one affirmatively and one negatively. The main result of this paper w…
K-polystable toric Fano varieties with small alpha invariants
Jihao Liu, Ziwen Zhu
For every , we exhibit an -dimensional K-polystable toric -Fano variety , defined by the face fan of an explicit lattice polytope, and whose alpha inva…
An equivariant fixed-level Demailly identity for Fano manifolds
Jihao Liu, Sheng Qin
Jin and Rubinstein asked whether the fixed-level equivariant Tian's alpha invariant equals the fixed-level equivariant global log canonical threshold, and proved this equality for…
Criteria for Weighted Homogeneity via Logarithmic Vector Fields
Jihao Liu, Xiping Zhang
Recently in [6] the authors proved a lower bound for the $\GSV$ index of a logarithmic vector field along an isolated hypersurface singularity and proposed a conjecture that the we…
A counterexample to the near-quadratic Elekes--Rónyai expander conjecture over
Jihao Liu
We disprove the near-quadratic Elekes--Rónyai expander conjecture over . The counterexample is a fixed nonspecial quadratic polynomial, together with arbitrarily large f…
Boundedness of total Cartier indices for rational singularities in families
Jihao Liu, Ruicheng Hu, Sheng Qin
We show that the total Cartier index of varieties with rational singularities in a bounded family is bounded. This solves a problem of Han and Jiang. The overall structure of the p…
Shokurov's global index conjecture for threefold foliations
Jihao Liu, Sheng Qin
We prove Shokurov's global index conjecture for foliations in dimension at most three. This answers a question of the first author, Meng, and Xie in dimension three. The main resul…
A question on klt type varieties of Han and Jiang
Jihao Liu
We prove that being of klt type is not an open condition in flat families of varieties. This answers a question of Han and Jiang. The construction in this paper substantially uses…
On a question of Mauri and Moraga
Jihao Liu
We give negative answers to both parts of a question of Mauri and Moraga on log Calabi-Yau pairs whose boundary decomposes into big divisors. The main result of this paper is obtai…
Optimal bend-and-break for foliations
Jihao Liu, Zeming Sun, Jiedong Jiang
We show that for every foliation of rank on a normal projective variety, the optimal constant in the bend-and-break inequality for tangent rational curves is $r+1…
An example of a very non-movable effective divisor
Jihao Liu
We give a negative answer to a question of Ciliberto, Knutsen, Lesieutre, Lozovanu, Miranda, Mustopa, and Testa on effective divisors of positive self-intersection on smooth projec…
On a question of Kollár and Kovács
Jihao Liu
We answer a question of Kollár and Kovács by constructing a flat projective morphism to a smooth curve whose fibers are Cohen--Macaulay and reduced, whose generic fiber is smooth,…
The minimal volume of stable surfaces of rank one
Jihao Liu, Wenfei Liu
We determine the minimal volume of a stable surface of rank one, and show that the surface attaining this minimum is unique up to isomorphism. This resolves a conjecture of Alexeev…
Examples of infinitely many -curves with higher genus on elliptic surfaces
Sichen Li, Jihao Liu
In this article, for every integer , we construct the first example of an elliptic surface with infinitely many smooth -curves of genus , settling an open question of…
Birational boundedness of stable families
Paolo Cascini, Jihao Liu, Calum Spicer +1
We prove that normal projective stable families of maximal variation, of fixed dimension, and with bounded adjoint volume are birationally bounded. This is a consequence of a subst…
Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
Jihao Liu, Zheng Xu
Assuming the abundance conjecture in dimension , we establish a non-algebraicity criterion of foliations: any log canonical foliation of rank with is not algebr…
Non-vanishing implies numerical dimension one abundance
Jihao Liu, Zheng Xu
We show that the non-vanishing conjecture implies the abundance conjecture when . We also prove the abundance conjecture in dimension when and …
Exceptional Fano varieties with small minimal log discrepancy
Louis Esser, Jihao Liu, Chengxi Wang
We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective sp…