Overview
- The first book to introduce topological methods of the theory of real algebraic varieties to non-specialists
- Presents both classical results and recent developments in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem
- Contains various levels of exercises with solutions to many of them provided at the end of each chapter
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (6 chapters)
Keywords
About this book
This book gives a systematic presentation of real algebraic varieties.
Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable.
This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book.
The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledgeis presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem.
Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Real Algebraic Varieties
Authors: Frédéric Mangolte
Translated by: Catriona Maclean
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-43104-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-43103-7Published: 22 September 2020
Softcover ISBN: 978-3-030-43106-8Published: 23 September 2021
eBook ISBN: 978-3-030-43104-4Published: 21 September 2020
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XVIII, 444
Number of Illustrations: 32 b/w illustrations, 28 illustrations in colour
Topics: Algebraic Geometry, Manifolds and Cell Complexes (incl. Diff.Topology), Several Complex Variables and Analytic Spaces