Local structure of algebraic monoids

2007/09/09 by Michel Brion, Brion, Michel · 2 citations
Computer Science · Mathematics · #14L10 #14L30 #14M17 #20M20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14L10 #msc:14L30 #msc:14M17 #msc:20M20

paper · pdf · doi:10.48550/arxiv.0709.1255

Final version, minor changes, to appear in Moscow Mathematical Journal

openalex publication_date 2007/09/09 · arxiv created 2008/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the local structure of an irreducible algebraic monoid M at an idempotent element e. When e is minimal, we show that M is an induced variety over the kernel MeM (a homogeneous space) with fibre the two-sided stabilizer M_e (a connected affine monoid having a zero element and a dense unit group). This yields the irreducibility of stabilizers and centralizers of idempotents when M is normal, and criteria for normality and smoothness of an arbitrary M. Also, we show that M is an induced variety over an abelian variety, with fiber a connected affine monoid having a dense unit group.

Cited by

• The ring of regular functions of an algebraic monoid
• Observable actions of algebraic groups

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