Answer by Ruadhaí Dervan for Are there examples of Fano manifolds such that...
This question was answered negatively by Kento Fujita today (at least when $G$ is trivial).Theorem (Fujita): If $\alpha(X,-K_X)=\frac{n}{n+1}$, then $X$ is K-stable and hence admits a Kähler-Einstein...
View ArticleAnswer by Ivan Cheltsov for Are there examples of Fano manifolds such that...
I see. THis is more subtle. There is no known example. I think it will be impossible or very hard to create one.Vanya
View ArticleAnswer by Ivan Cheltsov for Are there examples of Fano manifolds such that...
No, this is not sharp.General smooth cubic surface with Eckardt point is an example.Then Aut=Z_2, \alpha_G=2/3 and KE metric exists.If you want very non sharp example, use Kollar's paper...
View ArticleAre there examples of Fano manifolds such that Tian's alpha invariant...
The alpha invariant $\alpha(X)$ of a Fano manifold $X$ of dimension $n$ is defined as the infimum of log canonical thresholds of (effective) $\mathbb{Q}$-divisors $D\sim_{\mathbb{Q}}-K_X$. Similarly,...
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