Let X be an algebraic toric variety with respect to an action of an algebraic torus S. Let Σ be the corresponding fan. The aim of this paper is to investigate open subsets of X with a good quotient by the (induced) action of a subtorus T ⊂ S. It turns out that it is enough to consider open S-invariant subsets of X with a good quotient by T. These subsets can be described by subfans of Σ. We give a description of such subfans and also a description of fans corresponding to quotient varieties. Moreover, we give conditions for a subfan to define an open subset with a complete quotient space.
@article{bwmeta1.element.bwnjournal-article-cmv82i1p105bwm,
author = {Joanna \'Swi\k ecicka},
title = {Quotients of toric varieties by actions of subtori},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {105-116},
zbl = {0961.14032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p105bwm}
}
Święcicka, Joanna. Quotients of toric varieties by actions of subtori. Colloquium Mathematicae, Tome 79 (1999) pp. 105-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p105bwm/
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