Classification of the monomial Cremona transformations of the plane

TL;DR

This paper classifies all monomial Cremona transformations of the plane based on their multidegree, providing a comprehensive understanding of their structure and properties, and extends the classification to more general monomial maps.

Contribution

It offers a complete classification of monomial planar Cremona maps using multidegree, and extends results to broader classes of monomial maps.

Findings

Complete classification of monomial Cremona maps of the plane

Identification of properties of these maps

Extension to more general monomial transformations

Abstract

We classify all monomial planar Cremona maps by multidegree using recent methods developed by Aluffi. Following the main result, we prove several more properties of the set of these maps, and also extend the results to the more general `r.c. monomial' maps.