Work

Local inequalities for $cD$ and $cE$ singularities

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.28372

Authors: Chang, Chi-Kang, Chen, Jheng-Jie, Okada, Takuzo

Institutions: RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences, Kyushu University, National Central University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204790760

Cites: 1

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Related to: 10