Singularities of closures of spherical B-conjugacy classes of nilpotent orbits

2014/12/17 by Martin Bender, Nicolas Perrin, Bender, Martin +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.1412.5654

23 pages. Replaces arXiv:1412.5654. New results added

openalex publication_date 2014/12/17 · arxiv created 2016/04/08 · arxiv updated 2016/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for a simply laced group, the closure of the Borel conjugacy class of any nilpotent element of height 2 in its conjugacy class is normal and admits a rational resolution. We extend this, using Frobenius splitting techniques, to the closure in the whole Lie algebra if either the group has type A or the element has rank 2.

Citations

• Flags, Schubert polynomials, degeneracy loci, and determinantal formulas

Related

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• Orbit closures in flag varieties for the centralizer of an order-two nilpotent element : normality and resolutions for types A, B, D
• Spherical Nilpotent Orbits in Positive Characteristic
• Spherical conjugacy classes and involutions in the Weyl group
• A characterization of nilpotent orbit closures among symplectic singularities II