On existence of double coset varieties

DOI10.4064/CM126-2-3zbMATH Open1284.14059arXiv1111.5171OpenAlexW2964274961MaRDI QIDQ2884110

Artem Anisimov

Publication date: 24 May 2012

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Abstract: Let $G$ be a complex affine algebraic group and $H,FsubsetG$ be closed subgroups. The homogeneous space $G/H$ can be equipped with structure of a smooth quasiprojective variety. The situation is different for double coset varieties $dcosetsFGH$. In this paper we give examples showing that the variety $dcosetsFGH$ does not necessarily exist. We also address the question of existence of $dcosetsFGH$ in the category of constructible spaces and show that under sufficiently general assumptions $dcosetsFGH$ does exist as a constructible space.

Full work available at URL: https://arxiv.org/abs/1111.5171

zbMATH Keywords

categorical quotientcosetffine algebraic group

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Group actions on varieties or schemes (quotients) (14L30) Group actions on affine varieties (14R20)

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