The Gauss map of a projective foliation

TL;DR

This paper investigates the properties of the Gauss map associated with holomorphic codimension one foliations on projective spaces, focusing on the case where the Gauss map is birational, especially in three dimensions.

Contribution

It provides new insights into the behavior of the Gauss map for foliations on projective spaces, particularly characterizing when the map is birational.

Findings

Analysis of the Gauss map in the case n=3

Conditions under which the Gauss map is birational

Characterization of foliations with birational Gauss maps

Abstract

In this paper, we study the Gauss map of a holomorphic codimension one foliation on the projective space $\mathbb{P}^n$, $n\ge 2$, mainly the case $n=3$. Among other things, we will investigate the case where the Gauss map is birational.