Home of Haidong Liu

Publications:

[20] A note on Serrano's conjecture, to appear in Special Issue: AGEA2025, Taiwanese J. Math.;

[19] A Kawamata-Miyaoka type inequality for Fano varieties of arbitrary Picard number, arXiv:2511.13425, submitted;

[18] (with Chen Jiang) A canonical Fano threefold has Fano index ≤ 66, Proc. Lond. Math. Soc. (3) 133 (2026), no. 2, Paper No. e70195;

[17] Strictly nef divisors on singular K-trivial threefolds, Manuscripta Math. 177 (2026), no. 2, Paper No. 21, 14 pp;

[16] (with Chen Jiang and Jie Liu) Optimal upper bound for degrees of canonical Fano threefolds of Picard number one, J. Lond. Math. Soc. (2) 114 (2026), no. 2, Paper No. e70677;

[15] (with Jie Liu) Kawamata-Miyaoka type inequality for Q-Fano varieties with canonical singularities II: Terminal Q-Fano threefolds, Épijournal Géom. Algébrique 9 (2025), Art. 12, 21 pp;

[14] (with Jie Liu) Kawamata-Miyaoka type inequality for Q-Fano varieties with canonical singularities, J. Reine Angew. Math. 819 (2025), 265-281;

[13] (with Masataka Iwai and Chen Jiang) Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors, Sci. China Math. 68 (2025), no. 1, 1-18;

[12] On a numerical criterion for Fano fourfolds, Math. Res. Lett. 31 (2024), no. 4, 1133-1151;

[11] (with Shin-ichi Matsumura) Strictly nef divisors on K-trivial fourfolds, Math. Ann. 387 (2023), no. 1-2, 985-1008;

[10] (with Roberto Svaldi) Rational curves and strictly nef divisors on Calabi-Yau threefolds, Doc. Math. 27 (2022), 1581-1604;

[9] (with Chen Jiang) Boundedness of log pluricanonical representations of log Calabi-Yau pairs in dimension 2, Algebra Number Theory 15 (2021), no. 2, 545-567; 

[8] On the log canonical ring with Kodaira dimension two, Internat. J. Math. 31 (2020), no. 14, 2050121;

[7] (with Osamu Fujino) On the log canonical ring of projective plt pairs with the Kodaira dimension two, Ann. Inst. Fourier (Grenoble) 70 (2020), no. 4, 1775-1789;

[6] (with Osamu Fujino and Taro Fujisawa) Fundamental properties of basic slc-trivial fibrations II, Publ. Res. Inst. Math. Sci. 58 (2022), no. 3, 527-549;

[5] (with Osamu Fujino) Fujita-type freeness for quasi-log canonical curves and surfaces, Kyoto J. Math. 60 (2020), no. 4, 1453-1467;

[4] (with Osamu Fujino) Quasi-log canonical pairs are Du Bois, J. Algebraic Geom. 31 (2022), no. 1, 105-112;

[3] (with Osamu Fujino) On normalization of quasi-log canonical pairs, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 10, 97-101;

[2] Some remarks on log surfaces, Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 10, 115-119;

[1] Angehrn-Siu type effective base point freeness for quasi-log canonical pairs, Kyoto J. Math. 59 (2019), no. 2, 455-470.

Preprints:

[7] Kawamata-Miyaoka type inequality for weak Fano varieties, arXiv:2608.26597v1;

[6] On Fano indices of weighted projective spaces, arXiv:2608.03434v1;

[5] (with Chen Jiang) An effective upper bound for Fano indices of canonical Fano threefolds, I, arXiv:2505.19541 (superseded by Pub. [18]);

[4] On the log version of Serrano's conjecture, arXiv:2302.06209 (divided into Pub. [17] & [20]);

[3] On the existence of rational curves on projective hyperkahler fourfolds, arXiv:2111.04270v3;

[2] Remarks on very basic slc-trivial fibrations, arXiv:2004.12351;

[1] Fujita-type freeness for quasi-log canonical three-folds, arXiv:1902.08581.