F-alpha positivity conjecture for Q-Fano varieties

Let XX be a dd-dimensional Q\mathbb{Q}-Fano variety over C\mathbb{C}. Q-Fano F-alpha conjecture.

αF(X)>0.\alpha_F(X)>0.

This is a weaker global version of the positivity conjecture for log Fano pairs and remains open in general.

Sources & referencesView supporting material

Primary source

Shunsuke Takagi and Tatsuki Yamaguchi, “On the uniform positivity of F-signature under reduction modulo p”, arXiv:2507.16566 (2026).

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