A Partial Comparison of Stability Notions in K\"ahler Geometry
Differential Geometry
2018-12-31 v1
Abstract
In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of interest fit into this framework, in particular algebraic- and transcendental K-polystability, equivariant K-polystability, and the geodesic K-polystability notion introduced by the author in [46]. We provide a partial comparison of the above notions, and show equivalence of some of these notions provided that the underlying manifold satisfies a certain 'weak cscK' condition. As an application this proves K-polystability of a new family of cscK manifolds with irrational polarization.
Keywords
Cite
@article{arxiv.1812.10958,
title = {A Partial Comparison of Stability Notions in K\"ahler Geometry},
author = {Zakarias Sjöström Dyrefelt},
journal= {arXiv preprint arXiv:1812.10958},
year = {2018}
}
Comments
This is follow up work to arXiv:1711.11482