## About these proceedings

### Introduction

This proceedings volume gathers together selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry conference which was held at the Tokyo Metropolitan University on February 12-26, 2018, in Tokyo, Japan. In this book, the reader will find some of the latest research conducted by an international group of experts in affine and projective algebraic geometry. Topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. The articles contained in this volume will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as in certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.

### Keywords

affine variety locally nilpotent derivation automorphism group projective variety rational curve Ga-action Mathieu space Jacobian Conjecture log Kodaira dimension

### Editors and affiliations

- Shigeru Kuroda
- Nobuharu Onoda
- Gene Freudenburg

- 1.Department of Mathematical SciencesTokyo Metropolitan UniversityHachioji, TokyoJapan
- 2.Faculty of Applied PhysicsUniversity of FukuiFukuiJapan
- 3.Department of MathematicsWestern Michigan UniversityKalamazooUSA

#### About the editors

**Shigeru Kuroda** is a Professor at Tokyo Metropolitan University, Japan. Holding a PhD (2003) from Tohoku University, Japan, his main research focuses are on affine algebraic geometry and polynomial ring theory.

**Nobuharu Onoda** is a Professor at University of Fukui, Japan. He holds a PhD (1983) from Osaka University, Japan. His main research interests are in commutative algebra related to affine algebraic geometry.

**Gene Freudenburg** is a Professor at Western Michigan University, USA. He completed his PhD (1992) at Washington University, Saint Louis, USA. His chief research interests are in commutative algebra and affine algebraic geometry. He authored the Springer book “Algebraic Theory of Locally Nilpotent Derivations” (978-3-662-55348-0), now in its second edition.

### Bibliographic information