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arXiv · 1508.04578

Optimal bounds for the volumes of K\"ahler-Einstein Fano manifolds

Kento Fujita
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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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Kento Fujita. 2015-08-19. Optimal bounds for the volumes of K\"ahler-Einstein Fano manifolds. https://arxiv.org/abs/1508.04578

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