On the Miyaoka-Yau inequality for manifolds with nef anti-canonical line bundle

Abstract

Based on the recent work of K.~Zhang, we discuss the Miyaoka-Yau type inequality for projective manifolds with nef anti-canonical line bundle, assuming the lower bound of the delta-invariant introduced by Fujita and Odaka.

In the second version, we added the assumption about the numerical dimension to Theorem 1.3 (existence for cscK metrics). Some surface examples are appended. Comments on the equality condition for the Miyaoka-Yau inequality is updated