English

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

R2 v1 2026-06-21T19:59:40.741Z