Mahler measures, Stable Pairs, and the Global coercive estimate for the Mabuchi Functional
Differential Geometry
2021-05-05 v1 Algebraic Geometry
Abstract
We show that the Mabuchi energy of any polarized manifold (X,L) is (bounded below) proper on the full space of Kahler metrics in the first Chern class of L if and only if (X,L) is asymptotically (semi)stable. In particular it now follows from work of Xiuxiong Chen and Jinguri Cheng that there exists a cscK metric in the first Chern class of L if and only if (X,L) is asymptotically stable, provided the reduced automorphism group of (X,L) is finite.
Keywords
Cite
@article{arxiv.2105.01240,
title = {Mahler measures, Stable Pairs, and the Global coercive estimate for the Mabuchi Functional},
author = {Sean Timothy Paul},
journal= {arXiv preprint arXiv:2105.01240},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1910.06713