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b-stability

Proceedings of the Edinburgh Mathematical Society (1)

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b-Stability and Blow-Ups
S. K. Donaldson
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 1 / February 2014

Published online by Cambridge University Press:

23 December 2013, pp. 125-137
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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.