论文标题
关于Fano多型的Barycentric转换
On Barycentric transformations of Fano polytopes
论文作者
论文摘要
我们介绍了Fano多型的Barycentric转换的概念，我们可以从中为每个Fano多层分配一定的类型。可以将类型视为衡量给定的Fano多层接近Kähler-Einstein的程度的量度。特别是，我们希望每个Kähler-Einstein或对称的Fano Polytope均为$ b_ \ infty $。我们验证了一些低维情况的期望。我们强调，对于fano polytope $ x $ dimension $ 1 $，$ 3 $或$ 5 $，$ x $是kähler-einstein，仅当它是类型$ b_ \ infty $时。
We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be Kähler-Einstein. In particular, we expect that every Kähler-Einstein or symmetric Fano polytope is of type $B_\infty$. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope $X$ of dimension $1$, $3$ or $5$, $X$ is Kähler-Einstein if and only if it is of type $B_\infty$.
