On parametrization, optimization and triviality of test configurations

Details On parametrization, optimization and triviality of test configurations On parametrization, optimization and triviality of test configurations

2012-01-03

arxiv.org/abs/1201.0692v3

Mathematics

Algebraic Geometry

8 pages. Proposition 3.5 is corrected in v3

Scientific paper

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.

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