We classify all minimal models X of dimension n , Kodaira dimension n-1{n-1} and with vanishing Chern number c1n-2⁢c2⁢(X)=0{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{\epsilon>0} such that any minimal threefold satisfies either c1⁢c2=0{c_{1}c_{2}=0} or -c1⁢c2>ϵ{-c_{1}c_{2}>\epsilon}. This settles completely a conjecture of Kollár.

中文翻译：

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非一般类型情况下 Bogomolov-Miyaoka-Yau 不等式中的等式

我们对维度为n，小平维度为n-1 {n-1}且具有消失的陈恩数c1n-2⁢c2⁢（X）= 0 {c_ {1} ^ {n-2} c_ {2}的所有最小模型X进行分类}(X)=0}。这解决了 Kollár 的问题。完成 Kollár 和 Grassi 之前的工作，我们还表明存在一个通用常数 ϵ>0{\epsilon>0} 使得任何最小三重满足 c1⁢c2=0{c_{1}c_{2}=0}或-c1⁢c2> ϵ {-c_ {1} c_ {2}> \ epsilon}。这完全解决了 Kollár 的猜想。