$2^n-$rational maps

TL;DR

This paper introduces a new class of high-dimensional involutive rational maps called $2^n$-rational maps, extending the concept of quadrirational maps to arbitrary dimensions with symmetric properties.

Contribution

It constructs a broad family of $2^n$-rational maps, generalizing nondegenerate rational maps to higher dimensions with involutive and symmetric features.

Findings

Maps are involutions by construction

Maps and their companions share the same functional form

Rich family of $2^n$-rational maps demonstrated

Abstract

We present a natural extension of the notion of nondegenerate rational maps (quadrirational maps) to arbitrary dimensions. We refer to these maps as $2^n-$rational maps. In this note we construct a rich family of $2^n-$rational maps. These maps by construction are involutions and highly symmetric in the sense that the maps and their companion maps have the same functional form.