Monomial Cremona transformations and toric polar maps

TL;DR

This paper investigates monomial Cremona transformations in three-dimensional projective space, establishing an upper bound on the degree of their inverses, which enhances understanding of their algebraic and geometric properties.

Contribution

It proves that the inverse of a monomial Cremona transformation in three dimensions has degree at most d^2 - d + 1, providing a new bound in this area.

Findings

Inverse degree bounded by d^2 - d + 1

Improves understanding of monomial Cremona transformations

Establishes new degree bounds for inverse maps

Abstract

Given a birational map in the three dimensional projective space defined by monomials of degree $d$, we prove that its inverse is defined by monomials of degree at most $d^2-d+1$.