A new construction of D₅-singularities and generalization of Slodowy slices

2012/09/25 by K. Nakamoto, Koji Nakamoto, Nakamoto, K. +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG

paper · pdf · doi:10.48550/arxiv.1209.5541

19 pages

arxiv created 2012/09/25 · openalex publication_date 2012/09/25 · arxiv updated 2012/09/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Any simple elliptic singularity of type D₅ can be obtained by taking the intersection of the nilpotent variety and the 4-dimensional "good slices" in the semi-simple Lie algebra \frak sl(2, \mathbb C) ⊕ \frak sl(2, \mathbb C). We describe these new slices purely by the structure of the Lie algebra. We also construct the semi-universal deformation spaces of D₅-singularities by using the 4-dimensional "good slices".

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