Geodesic
Quotients of toric varieties by actions of subtori
Colloquium Mathematicum, Tome 82 (1999) no. 1, pp. 105-116
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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.
DOI : 10.4064/cm-82-1-105-116
Keywords: group actions, quotients, orbit spaces 
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Joanna Święcicka. Quotients of toric varieties by actions of subtori. Colloquium Mathematicum, Tome 82 (1999) no. 1, pp. 105-116. doi: 10.4064/cm-82-1-105-116

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