ArticleOriginal scientific text

Title

Quotients of toric varieties by actions of subtori

Authors 1

Affiliations

  1. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

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.

Keywords

group actions, quotients, orbit spaces

Bibliography

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Pages:
105-116
Main language of publication
English
Received
1998-07-10
Accepted
1999-05-14
Published
1999
Exact and natural sciences