Isotrivial unfoldings and structural theorems for foliations on Projective spaces

TL;DR

This paper investigates the structure of algebraic foliations on projective spaces through the study of unfoldings, especially those related to trivial families, providing new insights into their geometric properties.

Contribution

It introduces a detailed analysis of unfoldings of algebraic foliations and applies these results to understand the structure of foliations on projective spaces.

Findings

Unfoldings related to trivial families characterize certain foliation structures.

Structural theorems for foliations on projective spaces are established.

The relationship between unfoldings and foliation families is clarified.

Abstract

Following T. Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then applied to obtain information on the structure of foliations on projective spaces.