Equality in the Bogomolov--Miyaoka--Yau inequality in the non-general type case

Feng Hao; Stefan Schreieder

paper

Equality in the Bogomolov--Miyaoka--Yau inequality in the non-general type case

arXiv:2003.14020

Abstract

We classify all minimal models X of dimension n, Kodaira dimension n-1 and with vanishing Chern number $c_{1}^{n - 2} c_{2} (X) = 0$ . This solves a problem of Kollár. Completing previous work of Kollár and Grassi, we also show that there is a universal constant $ε > 0$ such that any minimal threefold satisfies either $c_{1} c_{2} = 0$ or $- c_{1} c_{2} > ε$ . This settles completely a conjecture of Kollár.

34 pages, Corollary 1.2(d) added, final version to appear in Crelle's Journal