Asian Journal of Mathematics

Volume 22 (2018)

Number 3

Special issue in honor of Ngaiming Mok (2 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

About J-flow, J-balanced metrics, uniform J-stability and K-stability

Pages: 391 – 412

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n3.a1

Authors

Yoshinori Hashimoto (Data4C’s K. K., Tokyo, Japan; and Aix Marseille Université, Marseille, France)

Julien Keller (Aix Marseille Université, Marseille, France)

Abstract

From the work of Dervan–Keller, there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan–Keller. We also obtain various criteria that imply uniform J-stability and uniform K-stability, strengthening the results of Dervan–Keller. Eventually, we discuss the case of Kähler classes that may not be integral over a compact manifold.

Keywords

J-flow, balanced metrics, uniform K-stability, J-stability, constant scalar curvature Kähler metrics

2010 Mathematics Subject Classification

14L24, 32Q15, 32Q25, 53C25, 53D50

Full Text (PDF format)

Received 14 November 2016

Accepted 4 July 2017

Published 8 August 2018