Real Algebraic Varieties

This book provides a systematic presentation of real algebraic varieties, intended for two kinds of audiences: beginners and advanced readers. It covers the basics of algebra and geometry, as well as major developments in the topology and geometry of varieties of dimension two and three.

Format: Paperback
Length: 464 pages
Publication date: 23 September 2021
Publisher: Springer Nature B.V.

Real algebraic varieties are incredibly important and ubiquitous in the world of mathematics. They play a crucial role in understanding coordinates, equations, and various mathematical concepts. However, the systematic study of these objects, despite their elementary nature, can be quite formidable. This book is designed to cater to two distinct audiences: firstly, it serves as a valuable guide for readers who have a solid foundation in algebra and geometry at the master's level, helping them grasp the basics of this rich theory. Secondly, it offers advanced readers a comprehensive overview of the field, presenting many fundamental results that are often overlooked in the available literature. One of the unique features of this book is its introduction of topological methods to non-specialists, making the theory more accessible and engaging.

The first three chapters provide a solid foundation by introducing the basics and classical methods of real and complex algebraic geometry. These chapters cover essential topics such as algebraic structures, vector spaces, and linear transformations. The last three chapters delve into specific aspects of real algebraic varieties. Each chapter focuses on a particular topic, allowing for a comprehensive overview of the field. The panorama of classical knowledge presented in these chapters is accompanied by significant developments in the topology and geometry of varieties of dimension two and three. The book also pays special attention to curves, which are considered the central subject of Hilbert's famous sixteenth problem.

Throughout the book, various levels of exercises are provided to assist readers in understanding the concepts and applying them. Additionally, the solutions of many of these exercises are provided at the end of each chapter, making it easier for readers to follow along and verify their understanding.

In conclusion, this book is an essential resource for anyone interested in learning about real algebraic varieties. It offers a systematic presentation of the theory, catering to both novice and advanced readers. With its comprehensive coverage, engaging writing style, and extensive exercises, it provides a valuable tool for anyone seeking to deepen their understanding of this fascinating field.

Weight: 646g
Dimension: 234 x 156 (mm)
ISBN-13: 9783030431068