Nilpotent commuting varieties of reductive Lie algebras

• 成果类型: Article
• 署名作者: Premet, A
• 署名单位: University of Manchester
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0315-6
• 发表日期: 2003
• 页码: 653-683
• 关键词: unipotent classes; ELEMENTS; Orbits; FIELDS

摘要

Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p greater than or equal to 0, and g = Lie G. In positive characteristic, suppose in addition that p is good for G and the derived subgroup of G is simply connected. Let N = N(g) denote the nilpotent variety of g, and C-nil(g) := {(x,y) is an element of N x N \ [x, y] = 0}, the nilpotent commuting variety of g. Our main goal in this paper is to show that the variety C-nil(g) is equidimensional. In characteristic 0, this confirms a conjecture of Vladimir Baranovsky; see [2]. When applied to GL(n), our result in conjunction with an observation in [2] shows that the punctual (local) Hilbert scheme H-n subset of Hilb(n)(P-2) is irreducible over any algebraically closed field.