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Greatest lower bounds on the Ricci curvature of Fano manifolds

Part of: Global differential geometry

Published online by Cambridge University Press:  17 August 2010

Gábor Székelyhidi
Gábor Székelyhidi*
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA (email: [email protected])
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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 ω∈c1(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.

Keywords

Kähler manifoldsRicci curvatureFano manifolds

MSC classification

Secondary: 53C55: Hermitian and Kählerian manifolds 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 1 , January 2011 , pp. 319 - 331
Copyright
Copyright © Foundation Compositio Mathematica 2010

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