Inverses of monomial Cremona maps

TL;DR

This paper investigates the degrees of inverses of monomial Cremona maps, revealing that inverse degrees can be large and non-contiguous, and provides a straightforward method for inversion.

Contribution

It characterizes the possible degrees of inverses of monomial Cremona maps and introduces an easy inversion method.

Findings

Inverse degrees can be significantly larger than the original degree.

The degrees of inverses do not always form a continuous range.

A simple method for inverting monomial Cremona maps is provided.

Abstract

We show that monomial Cremona maps of degree d on P^n can have inverses whose degree d' is quite large (for d > 2, d' = ((d-1)^n - 1)/(d-2) occurs), and that the full list of degrees d' does not always form an interval. An easy method for inverting the maps is presented.