Mathematical Research Letters

Volume 29 (2022)

Number 3

On the finiteness of ample models

Pages: 763 – 784



Junpeng Jiao (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)


In this paper, we generalize the finiteness of models theorem in [2] to Kawamata log terminal pairs with fixed Kodaira dimension. As a consequence, we prove that a Kawamata log terminal pair with $\mathbb{R}$-boundary has a canonical model, and it can be approximated by log pairs with $\mathbb{Q}$-boundary and the same canonical model.

Received 24 July 2020

Accepted 12 February 2021

Published 30 November 2022