Haidong Liu

activity

20162026

most citedMiyaoka type inequality for terminal threefolds with nef anti-canonical divisors

12 citations · 63 across the 25 of their papers we have counts for

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4 papers · 1 filter

math.AG2025

A Kawamata--Miyaoka type inequality for Fano varieties of arbitrary Picard number

Haidong Liu

Let $X$ be a $Q$ -factorial canonical weak Fano variety of dimension $n \geq 2$ . We show that if the $Q$ -Fano index $q_{Q} (X) \geq 3$ , then $X$ satisfies a Kaw…

math.AG2025

A canonical Fano threefold has Fano index $\leq 66$

Chen Jiang, Haidong Liu

We show that the $Q$ -Fano index of a canonical weak Fano $3$ -fold is at most $66$ . This upper bound is optimal and gives an affirmative answer to a conjecture of Chengxi W…

math.AG2025

An effective upper bound for Fano indices of canonical Fano threefolds, I

Chen Jiang, Haidong Liu

Let $X$ be a $Q$ -factorial weak Fano $3$ -fold with at worst isolated canonical singularities. We show that the $Q$ -Fano index of $X$ is at most $61$ .

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 $Q$ -factorial canonical Fano $3$ -fold $X$ of Picard number $1$ , $(- K_{X})^{3} \leq 72$ . The main tool is a Kawamata--Miyaoka type inequality which relates $(-…

A Kawamata--Miyaoka type inequality for Fano varieties of arbitrary Picard number

A canonical Fano threefold has Fano index ≤66

An effective upper bound for Fano indices of canonical Fano threefolds, I

Optimal upper bound for degrees of canonical Fano threefolds of Picard number one

A canonical Fano threefold has Fano index $\leq 66$