Greatest lower bounds on the Ricci curvature of Fano manifolds

Details Greatest lower bounds on the Ricci curvature of Fano manifolds Greatest lower bounds on the Ricci curvature of Fano manifolds

2009-03-31

arxiv.org/abs/0903.5504v1

Mathematics

Differential Geometry

12 pages

Scientific paper

On a Fano manifold M we study the supremum of the possible t such that there
is a K\"ahler metric in c_1(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 K\"ahler-Einstein metrics. We show that on P^2 blown up in one
point this supremum is 6/7, and we give upper bounds for other manifolds.

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