On Cremona Transformations of P^3 with all possible bidegrees

TL;DR

This paper constructs specific Cremona transformations of projective 3-space with various bidegrees, expanding the understanding of their possible degree pairs within certain bounds.

Contribution

It introduces a method to construct Cremona transformations of P^3 with all bidegrees satisfying particular inequalities, broadening the known spectrum of such transformations.

Findings

Constructed Cremona transformations with bidegrees (d,e) where d<e^2+1 and e< d^2+1

Demonstrated the existence of transformations for all positive d,e within these bounds

Extended the classification of Cremona transformations in P^3

Abstract

We construct Cremona transformations of P^3 with bidegrees (d,e), where d<e^2+1, e< d^2+1 and d,e> 0.