Publications and Preprints
In reverse chronological order by arXiv posting date.
2026
72. Disproof of the Yau–Tian–Donaldson conjecture
Jihao Liu
Note. For general polarized varieties, this disproves Donaldson’s 2002 cscK YTD conjecture even after the standard modern repairs to test configurations (normality and the product-in-codimension-two equality convention). The (log) Fano Kähler–Einstein YTD theorem and recent uniform/completed cscK YTD results are unaffected.
71. Mori dream Jacobian elliptic surfaces of Kodaira dimension one
Antonio Laface, Sichen Li, Jihao Liu
70. A klt generalized pair with infinitely generated canonical ring
Jihao Liu, Yanze Wang
69. The equality case of Ehrhart’s volume conjecture
Jihao Liu
68. Removing the Torsion-free Hypothesis in a Positivity Theorem on Deligne-Mumford Stacks
Shengyu Hou, Jihao Liu
67. Twelve common flex lines in a general pencil of cubics
Jihao Liu, Yanze Wang
66. Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Jihao Liu, Guoxiong Gao, Zeming Sun, Bin Wu, Shurui Liu, Jiedong Jiang, Haocheng Ju, Leheng Chen, Ronnie Cheng, Xiping Zhang, Bin Dong
65. A counterexample to the odd-dimensional rank bound for abelian p-group actions
Jihao Liu, Yanze Wang
64. On two questions of Qi on saturated filtrations
Jihao Liu, Haofeng Zhang
63. A slope-unstable bundle on a surface with 1-homogeneous projectivization
Jihao Liu
62. K-polystable toric Fano varieties with small alpha invariants
Jihao Liu, Ziwen Zhu
61. An equivariant fixed-level Demailly identity for Fano manifolds
Jihao Liu, Sheng Qin
60a. A Criteria of Weighted Homogeneity via Logarithmic Vector Fields
Jihao Liu, Xiping Zhang
Not AI-generated. Presents the same result as no. 60b; the mathematics is identical.
60b. Criteria of isolated weighted homogeneous hypersurface singularities using Logarithmic vector fields
Jihao Liu, Xiping Zhang
AI-generated (human-verified). Presents the same result as no. 60a; the mathematics is identical.
59. A counterexample to the near-quadratic Elekes–Rónyai expander conjecture over ℝ
Jihao Liu
58. Examples of infinitely many (-1)-curves with higher genus on elliptic surfaces
Sichen Li, Jihao Liu
57. Boundedness of total Cartier indices for rational singularities in families
Jihao Liu, Ruicheng Hu, Sheng Qin
56. Shokurov's global index conjecture for threefold foliations
Jihao Liu, Sheng Qin
55. A question on klt type varieties of Han and Jiang
Jihao Liu
54. On a question of Mauri and Moraga
Jihao Liu
53. Optimal bounds in bend-and-break for foliations
Jihao Liu, Zeming Sun, Jiedong Jiang
52. An example of a very non-movable effective divisor
Jihao Liu
51. On a question of Kollár and Kovács
Jihao Liu
50. The minimal volume of stable surfaces of rank one
Jihao Liu, Wenfei Liu
49. Birational boundedness of stable families
Paolo Cascini, Jihao Liu, Calum Spicer, Roberto Svaldi
48. Existence of the minimal model program for log canonical generalized pairs
Zhengyu Hu, Jihao Liu
47. Dual complexes of qdlt Fano type models and strong complete regularity
Jihao Liu, Konstantin Loginov
2025
46. Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
Jihao Liu, Zheng Xu
45. Variation of algebraically integrable adjoint foliated structures
Paolo Cascini, Jihao Liu, Fanjun Meng, Roberto Svaldi, Lingyao Xie
44a. Boundedness in general type MMP and fivefold effective termination
Jingjun Han, Jihao Liu, Lu Qi, Ziquan Zhuang
44b. Effective termination of general type MMPs in dimension at most five
Jingjun Han, Jihao Liu, Ziquan Zhuang
43. Sarkisov program for algebraically integrable and threefold foliations
Yifei Chen, Jihao Liu, Yanze Wang
Int. Math. Res. Not. 2026, no. 6, 1–19.
42. Non-vanishing implies numerical dimension one abundance
Jihao Liu, Zheng Xu
41. On finite generation and boundedness of adjoint foliated structures
Paolo Cascini, Jingjun Han, Jihao Liu, Fanjun Meng, Calum Spicer, Roberto Svaldi, Lingyao Xie
40. Classification of threefold enc cDV quotient singularities
Jingjun Han, Jihao Liu
2024
39. A generalized non-vanishing theorem for surfaces
Jihao Liu, Lingyao Xie
Pure Appl. Math. Q. (special volume in honor of Caucher Birkar), 22 (2026), no. 1, 235–244.
38. Flop between algebraically integrable foliations on potentially klt varieties
Yifei Chen, Jihao Liu, Yanze Wang
Int. J. Math. (2025), 2550035.
37. ACC for local volumes
Jingjun Han, Jihao Liu, Lu Qi
36. Minimal model program for algebraically integrable adjoint foliated structures
Paolo Cascini, Jingjun Han, Jihao Liu, Fanjun Meng, Calum Spicer, Roberto Svaldi, Lingyao Xie
35. Volume of algebraically integrable foliations and locally stable families
Jingjun Han, Junpeng Jiao, Mengchu Li, Jihao Liu
Trans. Amer. Math. Soc. 379 (2026), no. 10, 6809–6832.
34. Exceptional Fano varieties with small minimal log discrepancy
Louis Esser, Jihao Liu, Chengxi Wang
Math. Res. Lett. 33 (2026), no. 1, 161–198.
33. Minimal model program for algebraically integrable foliations on klt varieties
Jihao Liu, Fanjun Meng, Lingyao Xie
Compos. Math. 161 (2025), 3213–3276.
2023
32. On the equivalence between the effective adjunction conjectures of Prokhorov–Shokurov and of Li
Jingjun Han, Jihao Liu, Qingyuan Xue
Algebra Number Theory 19 (2025), no. 11.
31. On explicit bounds of Fano threefolds
Caucher Birkar, Jihao Liu
J. Reine Angew. Math. (Crelle's Journal) (2025).
30. Minimal model program for algebraically integrable foliations and generalized pairs
Guodu Chen, Jingjun Han, Jihao Liu, Lingyao Xie
29. The minimal volume of surfaces of log general type with non-empty non-klt locus
Jihao Liu, Wenfei Liu
To appear in Algebr. Geom.
28. ACC for lc thresholds for algebraically integrable foliations
Omprokash Das, Jihao Liu, Roktim Mascharak
Selecta Math. (N.S.) 32 (2026), no. 4, Paper No. 70, 34 pp.
27. Uniform rational polytopes of foliated threefolds and the global ACC
Jihao Liu, Fanjun Meng, Lingyao Xie
J. Lond. Math. Soc. 109 (2024), no. 6, e12950.
26. Optimal bounds on surfaces
Jihao Liu, Vyacheslav V. Shokurov
To appear in Algebraic Geometry and Physics.
25. Vanishing theorems for generalized pairs
Bingyi Chen, Jihao Liu, Lingyao Xie
24. Complements, index theorem, and minimal log discrepancies of foliated surface singularities
Jihao Liu, Fanjun Meng, Lingyao Xie
Eur. J. Math. 10 (2024), no. 6.
23. On global ACC for foliated threefolds
Jihao Liu, Yujie Luo, Fanjun Meng
Trans. Amer. Math. Soc. 376 (2023), no. 12, 8939–8972.
22. On effective Iitaka fibrations and existence of complements
Guodu Chen, Jingjun Han, Jihao Liu
Int. Math. Res. Not. (2024), no. 10, 8329–8349.
2022
21. Semi-ampleness of NQC generalized log canonical pairs
Jihao Liu, Lingyao Xie
Adv. Math. 427 (2023), 109126.
20. On termination of flips and exceptionally non-canonical singularities
Jingjun Han, Jihao Liu
Geom. Topol. 29 (2025), no. 1, 399–441.
19. Infinitesimal structure of log canonical thresholds
Jihao Liu, Fanjun Meng, Lingyao Xie
Doc. Math. 29 (2024), no. 3, 703–732.
18. Remark on complements on surfaces
Jihao Liu
Forum Math. Sigma 11 (2023), e42.
17. Uniform rational polytopes for Iitaka dimensions
Guodu Chen, Jingjun Han, Jihao Liu
In: Higher Dimensional Algebraic Geometry: A Volume in Honor of V. V. Shokurov (C. D. Hacon, C. Xu eds.), London Math. Soc. Lecture Note Series, Cambridge University Press (2025), 43–68.
16. Relative Nakayama–Zariski decomposition and minimal models for generalized pairs
Jihao Liu, Lingyao Xie
Peking Math. J. (2025), no. 8, 299–349.
15. Second largest accumulation point of minimal log discrepancies of threefolds
Jihao Liu, Yujie Luo
14. On the fixed part of pluricanonical systems for surfaces
Jihao Liu, Lingyao Xie
Math. Nachr. 296 (2023), 2046–2069.
13. On generalized lc pairs with b-log abundant nef part (with an Appendix by J. Han)
Junpeng Jiao, Jihao Liu, Lingyao Xie
Front. Math. (2025).
12. ACC for minimal log discrepancies of terminal threefolds
Jingjun Han, Jihao Liu, Yujie Luo
Adv. Math. 480 (2025), 110457.
2021
11. Existence of flips for generalized lc pairs
Christopher D. Hacon, Jihao Liu
Camb. J. Math. 11 (2023), no. 4, 795–828.
10. Number of singular points on projective surfaces
Jihao Liu, Lingyao Xie
Chin. Ann. Math. Ser. B 46 (2025), 713–724.
9. Divisors computing minimal log discrepancies on lc surfaces
Jihao Liu, Lingyao Xie
Math. Proc. Camb. Philos. Soc. 175 (2023), no. 1, 107–128.
2020
8. On effective birationality for sub-pairs
Jingjun Han, Jihao Liu
Int. J. Math. 34 (2023), no. 6, Article No. 2350029.
2019
7. An optimal gap of minimal log discrepancies of threefold non-canonical singularities
Jihao Liu, Liudan Xiao
J. Pure Appl. Algebra 225 (2021), no. 9.
6. Bounded deformations of (ε, δ)-log canonical singularities
Jingjun Han, Jihao Liu, Joaquín Moraga
J. Math. Sci. Univ. Tokyo 27 (2020), no. 1, 1–28.
5. ACC for minimal log discrepancies of exceptional singularities
Jingjun Han, Jihao Liu, Vyacheslav V. Shokurov
Peking Math. J. (2024), 1–33.
2018
4. Accumulation point theorem for generalized log canonical thresholds
Jihao Liu
3. Toward the equivalence of the ACC for a-log canonical thresholds and the ACC for minimal log discrepancies
Jihao Liu
To appear in Algebraic Geometry and Physics.
2. Sarkisov program for generalized pairs
Jihao Liu
Osaka J. Math. 58 (2021), no. 4.
2017
1. On invariance of plurigenera for foliated surface pairs
Jihao Liu