论文标题
表征最小的抗典型体积的终端三倍的终端三倍，ii
Characterizing terminal Fano threefolds with the smallest anti-canonical volume, II
论文作者
论文摘要
J.〜A.〜Chen和M.〜Chen证明了终端$ 3 $ -fold $ x $满足$（-K_X）^3 \ geq \ geq \ frac {1} {330} $。我们表明，$ \ mathbb {q} $ - fortorial terminal fano $ 3 $ - fold $ x $，$ρ（x）= 1 $和$（ - k_x）^3 = \ frac {1} {1} {330} $是$ \ \ mathbb $ \ m mathbb in $ \ mathbb的加权超出$ 66 $ in $ \ mathbb {p} $ 66 $ in 通过同样的方法，我们还为其他$ x_ {6d} \ subset \ mathbb {p}（1，a，a，b，2d，3d，3d）$在iano-fletcher列表中的加权超曲面的示例提供了特征。也就是说，我们表明，如果$ \ mathbb {q} $ - fortorial terminal fano $ 3 $ -fold $ x $带$ρ（x）= 1 $具有与$ x_ {6d} $相同的数值数据，那么$ x $本身就是同一类型的加权超曲面。
It was proved by J.~A.~Chen and M.~Chen that a terminal Fano $3$-fold $X$ satisfies $(-K_X)^3\geq \frac{1}{330}$. We show that a $\mathbb{Q}$-factorial terminal Fano $3$-fold $X$ with $ρ(X)=1$ 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 $ρ(X)=1$ has the same numerical data as $X_{6d}$, then $X$ itself is a weighted hypersurface of the same type.
