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arXiv · 2608.28372

Local inequalities for $cD$ and $cE$ singularities

Chi-Kang Chang·Jheng-Jie Chen·Takuzo Okada
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Abstract

We obtain inequalities for isolated $cD_n, cE_6, cE_7$ and $cE_8$ singularities, analogues of the $4\mu^2/(n+1)$-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.

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Chi-Kang Chang, Jheng-Jie Chen, Takuzo Okada. 2026-08-28. Local inequalities for $cD$ and $cE$ singularities. https://arxiv.org/abs/2608.28372

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