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On Parametrization, optimization and triviality of test configurations

Author: Yuji Odaka
Journal: Proc. Amer. Math. Soc. 143 (2015), 25-33
MSC (2010): Primary 14L24; Secondary 32Q20
Published electronically: August 19, 2014
MathSciNet review: 3272728
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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 the 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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Yuji Odaka
Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-850, Japan

Received by editor(s): March 17, 2012
Received by editor(s) in revised form: February 26, 2013
Published electronically: August 19, 2014
Additional Notes: The author was partially supported by the Grant-in-Aid for Scientific Research (KAKENHI No. 21-3748) and the Grant-in-Aid for JSPS fellows (PD)
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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