A new addition to the zoo of isolated symplectic singularities

2025/05/30 by Callum Berry, Berry, Callum
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Graph theory and applications #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.24524

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give details of a new isolated symplectic singularity found in an affine chart in a crepant partial resolution of ℂ⁴/G₅, which is 4-dimensional, isolated, and locally simply-connected. We distinguish the new singularity among all known such by the fact that the projective tangent cone at the singularity is non-reduced. We also find all 12 of its ℚ-factorial terminalisations, in the process finding 24 for the quotient singularity ℂ⁴/G₅.

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