AI 中文总结
该研究推导了孤立$cD_n$、$cE_6$、$cE_7$、$cE_8$奇点的紧局部不等式，作为$cA_n$奇点对应不等式的类似物，并用以证明含单个$cD_n$奇点的几类Fano三维加权超曲面的双有理刚性。
AI 中文摘要
我们得到了孤立$cD_n$、$cE_6$、$cE_7$及$cE_8$奇点的不等式，它们是文献\cite{KOP}中孤立$cA_n$奇点的$4μ^2/(n+1)$不等式的类似物。这些不等式是紧的。借此我们证明了仅含终端商奇点和一个$cD_n$奇点的几类Fano三维加权超曲面的双有理刚性。
英文摘要
We obtain inequalities for isolated $cD_n, cE_6, cE_7$ and $cE_8$ singularities, analogues of the $4μ^2/(n+1)$-inequality for isolated $cA_n$ singularity in \cite{KOP}. These inequalities are sharp. This enables us to prove the birational rigidity of certain families of Fano $3$-fold weighted hypersurfaces, which contain only terminal quotient singularities and one $cD_n$ singularity.
Comments22 pages, comments welcome
