On existence of double coset varieties

Artem Anisimov. "On existence of double coset varieties." Colloquium Mathematicae 126.2 (2012): 177-185. <http://eudml.org/doc/284211>.

@article{ArtemAnisimov2012,
abstract = {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.},
author = {Artem Anisimov},
journal = {Colloquium Mathematicae},
keywords = {ffine algebraic group; categorical quotient; coset},
language = {eng},
number = {2},
pages = {177-185},
title = {On existence of double coset varieties},
url = {http://eudml.org/doc/284211},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Artem Anisimov
TI - On existence of double coset varieties
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 2
SP - 177
EP - 185
AB - 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.
LA - eng
KW - ffine algebraic group; categorical quotient; coset
UR - http://eudml.org/doc/284211
ER -