Let G be a complex affine algebraic group and H,F ⊂ G be closed subgroups. The homogeneous space G/H can be equipped with the structure of a smooth quasiprojective variety. The situation is different for double coset varieties F∖∖G//H. We give examples showing that the variety F∖∖G//H does not necessarily exist. We also address the question of existence of F∖∖G//H in the category of constructible spaces and show that under sufficiently general assumptions F∖∖G//H does exist as a constructible space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-3,
author = {Artem Anisimov},
title = {On existence of double coset varieties},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {177-185},
zbl = {1284.14059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-3}
}
Artem Anisimov. On existence of double coset varieties. Colloquium Mathematicae, Tome 126 (2012) pp. 177-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-3/