Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
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DOI：
10.1353/ajm.2018.0009
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发表时间：
2015-08
影响因子：
1.7
通讯作者：
Kento Fujita
中科院分区：
文献类型：
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作者：
Kento Fujita
证明了任意n维Ding半稳定Fano流形X满足反正则体积小于或等于（n+1）^n.此外，等式成立当且仅当$X$同构于$n$维射影空间。结合Berman的一个结果，我们得到了n维Kahler-Einstein Fano流形的反正则体积的最优上界.
abstract:We show that any $n$-dimensional Ding semistable Fano manifold $X$ 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. Together with a result of Berman, we get the optimal upper bound for the anti-canonical volumes of $n$-dimensional K\"ahler-Einstein Fano manifolds.