Uniform K-stability and asymptotics of energy functionals in K\"ahler geometry
Differential Geometry
2020-05-21 v5 Algebraic Geometry
Abstract
Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in K\"ahler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability.
Keywords
Cite
@article{arxiv.1603.01026,
title = {Uniform K-stability and asymptotics of energy functionals in K\"ahler geometry},
author = {Sébastien Boucksom and Tomoyuki Hisamoto and Mattias Jonsson},
journal= {arXiv preprint arXiv:1603.01026},
year = {2020}
}
Comments
New version with errata (an error was found in the proof of Theorem 5.6). The affected parts of the paper are marked in red