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- W4285044807 abstract "It was proved by J.~A.~Chen and M.~Chen that a terminal Fano $3$-fold $X$ satisfies $(-K_X)^3geq frac{1}{330}$. We show that a $mathbb{Q}$-factorial terminal Fano $3$-fold $X$ with $rho(X)=1$ and $(-K_X)^3=frac{1}{330}$ is a weighted hypersurface of degree $66$ in $mathbb{P}(1,5,6,22,33)$. By the same method, we also give characterizations for other $11$ examples of weighted hypersurfaces of the form $X_{6d}subset mathbb{P}(1,a,b,2d,3d)$ in Iano-Fletcher's list. Namely, we show that if a $mathbb{Q}$-factorial terminal Fano $3$-fold $X$ with $rho(X)=1$ has the same numerical data as $X_{6d}$, then $X$ itself is a weighted hypersurface of the same type." @default.
- W4285044807 created "2022-07-13" @default.
- W4285044807 creator A5006707718 @default.
- W4285044807 date "2022-07-08" @default.
- W4285044807 modified "2023-10-16" @default.
- W4285044807 title "Characterizing terminal Fano threefolds with the smallest anti-canonical volume, II" @default.
- W4285044807 doi "https://doi.org/10.48550/arxiv.2207.03832" @default.
- W4285044807 hasPublicationYear "2022" @default.
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