Maps of toric varieties in Cox coordinates

Understand

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 arieties in terms of their Cox coordinates.
• Introducing formal roots of polynomials is necessary even in the simplest examples.