On cubic birational maps of $\mathbb{P}^3_\mathbb{C}$

TL;DR

This paper investigates the structure of cubic birational maps in three-dimensional complex projective space, specifically describing the irreducible components for maps of certain bidegrees, advancing understanding of their geometric classification.

Contribution

It provides a detailed description of the irreducible components of the set of cubic birational maps of specified bidegrees in a3^3_\u0000a3, a novel classification in algebraic geometry.

Findings

Identified irreducible components for bidegree (3,3) maps.

Extended classification to bidegree (3,4) and (3,5) maps.

Enhanced understanding of the structure of birational maps in a3^3.

Abstract

We study the birational maps of $\mathbb{P}^3_\mathbb{C}$. More precisely we describe the irreducible components of the set of birational maps of bidegree $(3,3)$ (resp. $(3,4)$, resp. $(3,5)$).