On Cremona Transformations of P^3 which factorize in a minimal form

TL;DR

This paper classifies Cremona transformations of P^3 that factorize into at most two elementary links, providing a geometric description of eight distinct classes of such transformations.

Contribution

It identifies and describes eight classes of Cremona transformations of P^3 with minimal factorization, expanding understanding of their structure and classification.

Findings

Eight classes of Cremona transformations identified

Geometric descriptions provided for each class

Connections established between transformations and Fano 3-folds

Abstract

We consider Cremona transformations of the complex projective space of dimension 3 which factorize as a product of at most two elementary links of type II, without small contractions, connecting two Fano 3-folds. We show that there are essentially eight classes of such transformations and we give a geometric description of elements in each of these classes.