activity
20242026
collaborators

7 papers

math.AG2026

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…

math.AG2025

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 $(-…

math.AG2025

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…

math.AG2025

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…

math.AG2025

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…

math.AG2025

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 .