A swift introduction to holomorphic foliations with singularities

TL;DR

This paper provides an accessible introduction to the theory of holomorphic foliations with singularities, covering fundamental concepts, recent questions, and motivating new researchers in the field.

Contribution

It offers a self-contained overview of key ideas and recent developments in holomorphic foliations with singularities, serving as an entry point for new researchers.

Findings

Introduction to core concepts of holomorphic foliations

Discussion of recent open problems in the field

Guidance for further research in holomorphic foliations

Abstract

These are the notes of a series of lectures delivered by the author at the Graduate School of Mathematics of the University of Tokyo, during the month of October 2015. They were meant to be as self-contained as possible, taking into account time and space. The basic idea was to introduce the concepts and some of the basic results in the theory of holomorphic foliations with singularities. Another goal is to guide the reader to some of the recent questions and problems in the field, providing in this way a motivating introduction to those who are interested in studying a new subject.