Codimension one foliations with trivial canonical class on singular spaces II

TL;DR

This paper classifies certain complex geometric structures called codimension one foliations with trivial canonical class on singular varieties, and explores their birational geometry on threefolds, extending recent research in the field.

Contribution

It provides a detailed structure theorem for foliations with trivial canonical class on singular spaces and advances understanding of their birational properties on threefolds.

Findings

Classification of foliations with trivial canonical class on singular varieties.

Description of birational geometry of rank two foliations on threefolds.

Extension of recent results by Spicer and others in the field.

Abstract

In this article, we give the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with klt singularities. Building on recent works of Spicer, Cascini - Spicer and Spicer - Svaldi, we then describe the birational geometry of rank two foliations with canonical singularities and canonical class of numerical dimension zero on complex projective threefolds.