# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Quotients of toric varieties by actions of subtori

### Tom 82 / 1999

Colloquium Mathematicum 82 (1999), 105-116 DOI: 10.4064/cm-82-1-105-116

#### Streszczenie

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.

#### Autorzy

• Joanna Święcicka

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