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b-Stability and Blow-Ups

Published online by Cambridge University Press:  23 December 2013

S. K. Donaldson
S. K. Donaldson*
Affiliation:
Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2AZ, UK, (s.donaldson@imperial.ac.uk)
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Abstract

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We study a notion of ‘b-stability’, introduced previously by the author in connection with the existence of constant scalar curvature Kähler, and Kähler-Einstein, metrics. The main result is Theorem 1.2, which makes progress towards a statement that the existence of such metrics implies b-stability. The proof is a modification of an argument of Stoppa, taking account of the birational transformations involved in the definition of b-stability.

Keywords

Kähler–Einstein metricsbirational geometryb-stabilityPrimary 53C55Secondary 14J1014E99
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 125 - 137
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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