The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric varieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-3-2,
author = {Gavin Brown and Jaros\l aw Buczy\'nski},
title = {Maps of toric varieties in Cox coordinates},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {213-267},
zbl = {1312.14123},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-3-2}
}
Gavin Brown; Jarosław Buczyński. Maps of toric varieties in Cox coordinates. Fundamenta Mathematicae, Tome 220 (2013) pp. 213-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-3-2/