Special Test Configurations

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• Chenyang Xu (MIT)
• Wednesday 11 April 2012, 10:00-11:00
• MR2.

If you have a question about this talk, please contact Dr. J Ross.

(Joint with Chi Li) For any test configuration (TC) of a Fano manifold, we will use MMP theory to construct a new TC with the central fiber being a Q-Fano variety (in particular it’s normal) such that the Donaldson-Futaki invariant of the new TC is smaller than the original one after scaling by the factor of the base change. We call a TC with a Q-Fano central fiber a special TC. The above theorem gives an affirmative answer to Tian’s conjecture which says that to test K-(semi)stability of a Fano manifolds, it suffices to only test on special TC.

This talk is part of the Workshop on Kahler Geometry series.

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