Counting square free monomial cremona maps

TL;DR

This paper classifies all square-free Cremona maps with up to six variables and develops an algorithm to enumerate such transformations, extending the classification to seven variables.

Contribution

It provides a complete classification for up to six variables and introduces an algorithm to count monomial square-free Cremona transformations, extending to seven variables.

Findings

Complete list of square-free Cremona maps with ≤6 variables.

Algorithm for counting monomial square-free Cremona transformations.

Extended classification to 7 variables.

Abstract

We give a complete list of square-free Cremona maps with at most six variables, up to equivalence classes. We also build an algorithm to count monomial square-free Cremona transformations. Using this algorithm, we obtain a complete list of monomial square-free Cremona transformations in seven variables.