Sharp Polynomial Upper Bounds for Anticanonical Volumes

Pinxian Bie, Peien Du, Zhengjie Yu

For every positive integer $n$, we prove that there is a constant $C_n$, depending only on $n$, such that $Vol(-K_X)\le C_n{\epsilon }^{-(2^n-n-1)}$ whenever $X$ admits an $\epsilon$-lc log Fano…