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PreprintCC BY 4.0arXiv

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 cDn, cE6, cE7 and cE8 singularities, analogues of the 4μ2/(n+1)-inequality for isolated cAn 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 cDn singularity.

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Cite

BibTeXRIS
BibTeX
@misc{chang2026local,
  title = {{Local inequalities for $cD$ and $cE$ singularities}},
  author = {Chi-Kang Chang and Jheng-Jie Chen and Takuzo Okada},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.28372},
  eprint = {2608.28372},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28372},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Local inequalities for cD and cE singularities
AU  - Chi-Kang Chang
AU  - Jheng-Jie Chen
AU  - Takuzo Okada
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2608.28372
UR  - https://arxiv.org/abs/2608.28372
AB  - 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.
ER  -