12 citations · 63 across the 25 of their papers we have counts for
25 papers
Kawamata--Miyaoka type inequality for varieties with nef anticanonical divisor
Haidong Liu
Let be an -lc projective variety of dimension such that is nef and is a real number. Then for any nef divisors , \[ c_1(X)^{2…
On Fano indices of weighted projective spaces
Haidong Liu
The Sylvester sequence is defined recursively by and . In this paper, we prove that the Fano index of an -dimensional well-formed weighted pro…
A Kawamata--Miyaoka type inequality for Fano varieties of arbitrary Picard number
Haidong Liu
Let be a -factorial canonical weak Fano variety of dimension . We show that if the -Fano index , then satisfies a Kaw…
A canonical Fano threefold has Fano index
Chen Jiang, Haidong Liu
We show that the -Fano index of a canonical weak Fano -fold is at most . This upper bound is optimal and gives an affirmative answer to a conjecture of Chengxi W…
An effective upper bound for Fano indices of canonical Fano threefolds, I
Chen Jiang, Haidong Liu
Let be a -factorial weak Fano -fold with at worst isolated canonical singularities. We show that the -Fano index of is at most .
Optimal upper bound for degrees of canonical Fano threefolds of Picard number one
Chen Jiang, Haidong Liu, Jie Liu
We show that for a -factorial canonical Fano -fold of Picard number , . The main tool is a Kawamata--Miyaoka type inequality which relates $(-…
Kawamata-Miyaoka-type inequality for -Fano varieties with canonical singularities II: Terminal -Fano threefolds
Haidong Liu, Jie Liu
We prove an optimal Kawamata-Miyaoka-type inequality for terminal -Fano threefolds with Fano index at least . As an application, any terminal -Fano threefo…
Kawamata--Miyaoka type inequality for -Fano varieties with canonical singularities
Haidong Liu, Jie Liu
Let be an -dimensional normal -factorial projective variety with canonical singularities and Picard number one such that is smooth in codimension two, …
Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors
Masataka Iwai, Chen Jiang, Haidong Liu
In this paper, we study the Miyaoka type inequality on Chern classes of terminal projective -folds with nef anti-canonical divisors. Let be a terminal projective -fold su…
On the log version of Serrano's conjecture
Haidong Liu
In this paper, we continue the study of Serrano's conjecture in low dimensions. We focus on two special cases of the log version of Serrano's conjecture: the ampleness conjecture a…
On the existence of rational curves on projective hyperkähler fourfolds
Haidong Liu
We show that if is a projective hyperkähler fourfold and there exists a nonzero effective divisor which is not of bi-elliptic type and contained in the boundary of the nef…
On a numerical criterion for Fano fourfolds
Haidong Liu
In this paper, we prove a special case of Campana--Peternell's conjecture in dimension 4. Specifically, we show that a projective smooth fourfold with $c^2_1(X)\cdot c_2(X)\neq…
Strictly nef divisors on K-trivial fourfolds
Haidong Liu, Shin-ichi Matsumura
In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on…
Rational curves and strictly nef divisors on Calabi--Yau threefolds
Haidong Liu, Roberto Svaldi
We give a criterion for a nef divisor to be semiample on a Calabi--Yau threefold when and . As a direct consequence, we show that on suc…
Remarks on very basic slc-trivial fibrations
Haidong Liu
We study very basic slc-trivial fibrations. We show that restricting on any lc center of a very basic slc-trivial fibration, its moduli part is numerically trivial if and only if i…
Boundedness of log pluricanonical representations of log Calabi-Yau pairs in dimension 2
Chen Jiang, Haidong Liu
We show the boundedness of B-pluricanonical representations of lc log Calabi-Yau pairs in dimension . As applications, we prove the boundedness of indices of slc log Calabi-Yau…
On the log canonical ring in Kodaira dimension two
Haidong Liu
We prove that the log canonical ring of a projective log canonical pair in Kodaira dimension two is finitely generated.
Fujita-type freeness for quasi-log canonical threefolds
Haidong Liu
In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type…
On the log canonical ring of projective plt pairs with the Kodaira dimension two
Osamu Fujino, Haidong Liu
The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.
Fundamental properties of basic slc-trivial fibrations, II
Osamu Fujino, Taro Fujisawa, Haidong Liu
We prove that if the moduli -b-divisor of a basic slc-trivial fibration is b-numerically trivial then it is -b-linearly trivial. As a consequence, we prove th…
Fujita-type freeness for quasi-log canonical curves and surfaces
Osamu Fujino, Haidong Liu
We prove Fujita-type basepoint-freeness for projective quasi-log canonical curves and surfaces.
Quasi-log canonical pairs are Du Bois
Osamu Fujino, Haidong Liu
We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.
On normalization of quasi-log canonical pairs
Osamu Fujino, Haidong Liu
The normalization of a quasi-log canonical pair is a quasi-log canonical pair.
Some remarks on log surfaces
Haidong Liu
Fujino and Tanaka established the minimal model theory for -factorial log surfaces in characteristic and , respectively. We prove that every intermediate surface…