The aim of this paper is to construct open sets with good quotients by an action of a reductive group starting with a given family of sets with good quotients. In particular, in the case of a smooth projective variety X with Pic(X) = 𝒵, we show that all open sets with good quotients that embed in a toric variety can be obtained from the family of open sets with projective good quotients. Our method applies in particular to the case of Grassmannians.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-5,
author = {Joanna \'Swi\k ecicka},
title = {A combinatorial construction of sets with good quotients by an action of a reductive group},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {85-102},
zbl = {0963.14020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-5}
}
Joanna Święcicka. A combinatorial construction of sets with good quotients by an action of a reductive group. Colloquium Mathematicae, Tome 89 (2001) pp. 85-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-5/