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

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arxiv 2003.14020 v2 pith:GZLWA4EH submitted 2020-03-31 math.AG math.CV

Feng Hao , Stefan Schreieder This is my paper · ORCID
classification math.AGmath.CV
keywords kolldimensionepsilonminimalbogomolov--miyaoka--yaucasechernclassify
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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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  1. Foliated Minimal Models and Flops

    math.AG 2026-08 conditional novelty 8.0 of 10

    Rank one foliations with canonical singularities have unique minimal models; co-rank one threefolds admit D-flops in klt and F-dlt settings, while new examples show flops and canonical models can fail.

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