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The anticanonical volume of Gorenstein Fano fourfolds is bounded, with $\mathbb{P}(1,1,1,1,2)$ realizing the sharpest bound for terminal singularities.
The anticanonical volume of log Fano varieties scales polynomially with $\epsilon^{-1}$ with an exponent of $2^n-n-1$, a bound tight even for toric varieties.