Flows of birational quadratic transformations in the complex projective space of dimension 3

TL;DR

This paper classifies quadratic birational transformation flows in complex projective 3-space, revealing that all such flows preserve a pencil of planes through a line, advancing understanding of their geometric structure.

Contribution

It provides a classification of quadratic birational flows in complex projective 3-space and shows they all preserve a specific geometric configuration.

Findings

Every quadratic flow preserves a pencil of planes through a line

Classification of flows up to linear conjugation

Identification of geometric invariants of the flows

Abstract

We study and classify up to a linear conjugation germs of flows in the space of quadratic birational transformations of the complex projective space of dimension 3. As a consequence we show that every quadratic flow preserves a pencil of planes through a line.