# Field generators in two variables and birational endomorphisms of $\mathbb{A}^2$

## TL;DR

This paper surveys the topics of field generators and birational endomorphisms of the affine plane in two variables, including new insights, originating from Abhyankar's seminar in the 1970s.

## Contribution

It provides a comprehensive survey with significant new material on field generators and birational endomorphisms of the affine plane.

## Key findings

- Introduction of new results on field generators in two variables.
- In-depth analysis of birational endomorphisms of the affine plane.
- Historical context from Abhyankar's seminar in the 1970s.

## Abstract

This article is a survey of two subjects: the first part is devoted to field generators in two variables, and the second to birational endomorphisms of the affine plane. Each one of these subjects originated in Abhyankar's seminar in Purdue University in the 1970s. Note that the part on field generators is more than a survey, since it contains a considerable amount of new material.