On existence of double coset varieties

Details On existence of double coset varieties On existence of double coset varieties

2011-11-22

arxiv.org/abs/1111.5171v2

Mathematics

Algebraic Geometry

7 pages; this version incorporates additions suggested by a referee of Colloquium Mathematicum

Scientific paper

Let $G$ be a complex affine algebraic group and $H, F \subset G$ 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 $\dcosets{F}{G}{H}$. In this paper we give examples showing that the variety $\dcosets{F}{G}{H}$ does not necessarily exist. We also address the question of existence of $\dcosets{F}{G}{H}$ in the category of constructible spaces and show that under sufficiently general assumptions $\dcosets{F}{G}{H}$ does exist as a constructible space.

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