Birational maps preserving the contact structure on $\mathbb{P}^3_\mathbb{C}$

TL;DR

This paper investigates the group of birational maps on complex projective 3-space that preserve the contact structure, providing insights into their algebraic and geometric properties.

Contribution

It characterizes the birational maps of ^3 preserving the contact structure, advancing understanding of their structure and classification.

Findings

Identification of the subgroup of birational maps preserving contact structure

Structural properties of these automorphisms

Classification results for contact-preserving birational maps

Abstract

We study the group of polynomial automorphisms of $\mathbb{C}^3$ (resp. birational self-maps of $\mathbb{P}^3_\mathbb{C}$) that preserve the contact structure.