Quadro-quadric cremona transformations in low dimensions via the JC-correspondence

TL;DR

This paper classifies and describes new simple families of quadro-quadric Cremona transformations in low-dimensional projective spaces, providing explicit classifications in dimensions four and five.

Contribution

It introduces new simple families of quadro-quadric Cremona transformations and offers complete classifications in dimensions four and five.

Findings

Explicit classifications in dimension four

Explicit classifications in dimension five

Introduction of new simple families of transformations

Abstract

We apply the results of arXiv:1109.3573 to study quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension four and five.