The Miyaoka-Yau inequality on smooth minimal models

Abstract

In this short note, we offer an observation that the Miyaoka-Yau inequality holds for any compact Kähler manifold with nef canonical bundle, i.e. a smooth minimal model. It follows directly from the existence of cscK metrics in a neighborhood of the canonical class which was confirmed both by the work of Dyrefelt and Song using different approaches.

5 pages