Special Test Configurations (Chenyang Xu)

Duration: 53 mins 55 secs

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Created:

2012-04-24 09:22

Collection:

Workshop on Kahler Geometry

Publisher:

University of Cambridge

Dr J. Ross

Language:

eng (English)

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Author:

Chenyang Xu


Abstract:	(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.

Abstract:

(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.

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