On parametrization, optimization and triviality of test configurations

2012/01/03 by Odaka, Yuji · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.0692

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.

Cited by

• Lines in the space of Kähler metrics

Related

• A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations
• Filtrations and test-configurations
• A stronger concept of K-stability
• Uniform K-stability, Duistermaat-Heckman measures and singularities of\n pairs
• A generalization of Ross-Thomas' slope theory