English

Lifting of morphisms to quotient presentations

Algebraic Geometry 2007-05-23 v1 Commutative Algebra

Abstract

In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that this can be completely answered in terms of invariant divisors. As an application we prove that two toric varieties, which are isomorphic as abstract algebraic varieties, are even isomorphic as toric varieties. This generalizes a well-known result of Demushkin on affine toric varieties.

Keywords

Cite

@article{arxiv.math/0209406,
  title  = {Lifting of morphisms to quotient presentations},
  author = {Florian Berchtold},
  journal= {arXiv preprint arXiv:math/0209406},
  year   = {2007}
}

Comments

11 pages, to appear in manuscripta math

R2 v1 2026-07-22T16:48:01.419Z