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arXiv · 2003.14020

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

Feng Hao·Stefan Schreieder
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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 Koll\'ar. Completing previous work of Koll\'ar and Grassi, we also show that there is a universal constant $\epsilon>0$ such that any minimal threefold satisfies either $c_1c_2=0$ or $-c_1c_2>\epsilon$. This settles completely a conjecture of Koll\'ar.

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Feng Hao, Stefan Schreieder. 2020-03-31. Equality in the Bogomolov--Miyaoka--Yau inequality in the non-general type case. https://arxiv.org/abs/2003.14020

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