We consider constant scalar curvature K ̈ahler 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 K ̈ahler metric. We show that sequences of such metrics converge smoothly on compact subsets away from a subvariety to the singular K ̈ahler Einstein metric in the canonical class. This confirms partially a conjecture of Jian-Shi-Song about the convergence behavior of such sequences. In the meantime, we also present an application of the existence of cscK metrics on smooth minimal models to prove the Miyaoka-Yau inequality.

Creator

• Liu, Wanxing

DOI

• https://doi.org/10.21985/n2-txwh-bs75

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:16350
• etdadmin_upload_945453

Date created

• 2022-01-01

Resource type

• Dissertation

Rights statement

• In Copyright