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Greatest lower bounds on the Ricci curvature of Fano manifolds

Published online by Cambridge University Press:  17 August 2010

Gábor Székelyhidi*
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA (email: gabor@math.columbia.edu)
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Abstract

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On a Fano manifold M we study the supremum of the possible t such that there is a Kähler metric ωc1(M) with Ricci curvature bounded below by t. This is shown to be the same as the maximum existence time of Aubin’s continuity path for finding Kähler–Einstein metrics. We show that on P2 blown up in one point this supremum is 6/7, and we give upper bounds for other manifolds.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2010

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