On a variety related to the commuting variety of a reductive Lie algebra

2015/07/20 by Jean-Yves Charbonnel, Charbonnel, Jean-Yves · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1507.05419

openalex publication_date 2015/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a reductive Lie algbera over an algbraically closed field of charasteristic zero,we consider a borel subgroup B of its adjoint group, a Cartan subalgebra contained inthe Lie algebra of B and the closure X of its orbit under B in the Grassmannian.The variety X plays an important role in the study of the commuting variety. In thisnote, we prove that X is Gorenstein with rational singularities.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Cited by

• On the generalized commuting varieties of a reductive Lie algebra

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