Miyaoka-type inequalities for terminal threefolds with nef anti-canonical divisors  

作　　者：Masataka Iwai Chen Jiang Haidong Liu 

机构地区：[1]Department of Mathematics,Graduate School of Science,Osaka University,Osaka 560-0043,Japan [2]Shanghai Center for Mathematical Sciences&School of Mathematical Sciences,Fudan University,Shanghai 200438,China [3]Department of mathematics,Sun Yat-sen University,Guangzhou 510275,China

出　　处：《Science China Mathematics》2025年第1期1-18,共18页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China for Innovative Research Groups(Grant No.12121001);National Key Research and Development Program of China(Grant No.2020YFA0713200);supported by Grant-in-Aid for Early Career Scientists(Grant No.22K13907)。

摘　　要：In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical divisors.Let X be a terminal projective 3-fold such that-KX is nef.We show that if c_(1)(X)·c_(2)(X)≠0,then c_(1)(X)·c_(2)(X)≥1/252;if further X is not rationally connected,then c_(1)(X)·c_(2)(X)≥4/5 and this inequality is sharp.In order to prove this,we give a partial classification of such varieties along with many examples.We also study the nonvanishing of c_(1)(X)^(dim X-2)·c_(2)(X)for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.

关 键 词：terminal threefolds Miyaoka-type inequality BOUNDEDNESS 

分 类 号：O178[理学—数学]