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• 10 Are there examples of Fano manifolds such that Tian's alpha invariant satisfies $\alpha_G(X)=\frac{n}{n+1}$ but without a Kähler-Einstein metric?
• 8 Are there examples of Fano manifolds such that Tian's alpha invariant satisfies $\alpha_G(X)=\frac{n}{n+1}$ but without a Kähler-Einstein metric?
• 7 Fano manifold admit an smooth anti-canonical divisor?
• 6 Is there an extremal metric on toric Fano manifolds which have nonzero Futaki invariant?
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