On parametrization, optimization and triviality of test configurations
Algebraic Geometry
2012-02-21 v3 Differential Geometry
Abstract
We give a parametrization of test configurations in the sense of Donaldson via spherical buildings, and show the existence of "optimal" destabilizing test configurations for unstable varieties, in the wake of Mumford and Kempf. We also give an account of the recent slight amendment to definition of K-stability after Li-Xu, from two other viewpoints: from the one parameter subgroups and from the author's blow up formalism.
Keywords
Cite
@article{arxiv.1201.0692,
title = {On parametrization, optimization and triviality of test configurations},
author = {Yuji Odaka},
journal= {arXiv preprint arXiv:1201.0692},
year = {2012}
}
Comments
8 pages. Proposition 3.5 is corrected in v3