2006.288: Nilpotent commuting varieties of reductive Lie algebras

2006.288: Alexander Premet (2003) Nilpotent commuting varieties of reductive Lie algebras. Inventiones Mathematicae, 154 (3). pp. 653-683. ISSN 1432-1297

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DOI: 10.1007/s00222-003-0315-6

Abstract

Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic pge0, and gfr=LiethinspG. In positive characteristic, suppose in addition that p is good for G and the derived subgroup of G is simply connected. Let Nscr=Nscr(gfr) denote the nilpotent variety of gfr, and Cfrnil(gfr):={(x,y)isinNscr×Nscrthinsp|thinspthinsp[x,y]=0}, the nilpotent commuting variety of gfr. Our main goal in this paper is to show that the variety Cfrnil(gfr) 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 hamilt n subHilb n (Popf2) is irreducible

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