Wanxing Liu | Searcharxiv

arXiv2021

Convergence of cscK metrics on smooth minimal models of general type

We consider constant scalar curvature Kähler metrics on a smooth minimal model of general type in a neighborhood of the canonical class, which is the perturbation of the canonical class by a fixed Kähler metric. We show that sequences of such metrics converge smoothly on compact subsets away from a subvariety to the singular Kähler Einstein metric in the canonical class. This confirms partially a conjecture of Jian-Shi-Song about the convergence behavior of such sequences.

math.DG↗

arXiv2020

The Miyaoka-Yau inequality on smooth minimal models

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.

math.DG↗