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Bulletin of the London Mathematical Society Advance Access originally published online on December 15, 2006
Bulletin of the London Mathematical Society 2007 39(1):76-84; doi:10.1112/blms/bdl015
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© 2006 London Mathematical Society

Extremal metrics and K-stability

Gábor Székelyhidi

Department of Mathematics
Imperial College
London SW7 2AZ
United Kingdom
gabor.szekelyhidi{at}ic.ac.uk

Received 4 October 2005. Revision received 27 January 2006.

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kähler metric. This generalises conjectures by Yau, Tian and Donaldson, which relate to the case of Kähler–Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates this conjecture, and an example computation that supports it.


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