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

Abstract: We classify all good minimal models of dimension n and with vanishing Chern number $c_1^{n-2}c_2(X)=0$, which corresponds to equality in the Bogomolov-Miyaoka—Yau inequality in the non-general type case. Here the most interesting case is that of Kodaira dimension n-1, where any minimal model is known to be good. Our result solves completely a problem a Kollar. In dimension three, our approach together with previous work of Grassi and Kollar also leads to a complete solution of a conjecture of Kollar, asserting that on a minimal threefold, c_1c_2 is either zero or universally bounded away from zero. Joint work with Feng Hao.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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