The Miyaoka-Yau inequality on smooth minimal models

TL;DR

This paper demonstrates that the Miyaoka-Yau inequality applies to smooth minimal models with nef canonical bundles, leveraging recent results on the existence of constant scalar curvature Kähler metrics.

Contribution

It establishes the Miyaoka-Yau inequality for all smooth minimal models with nef canonical bundles, based on recent advances in Kähler geometry.

Findings

Miyaoka-Yau inequality holds for smooth minimal models

Existence of cscK metrics near the canonical class confirmed

Inequality applies to compact Kähler manifolds with nef canonical bundle

Abstract

In this short note, we offer an observation that the Miyaoka-Yau inequality holds for any compact K\"{a}hler 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.