Optimal bounds for the volumes of Kähler-Einstein Fano manifolds (1508.04578v1)

Published 19 Aug 2015 in math.AG and math.DG

Abstract: We show that any $n$-dimensional Fano manifold $X$ admitting K\"ahler-Einstein metrics satisfies that the anti-canonical volume is less than or equal to the value $(n+1)^n$. Moreover, the equality holds if and only if $X$ is isomorphic to the $n$-dimensional projective space.

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Authors (1)

Kento Fujita

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