Overview
Explains the motivations behind concepts as they arise, often comparing them to their counterparts in other areas of mathematics
Includes foundational concepts from commutative algebra and details their origins. The concept of regularity is one key example
Shows readers a path toward more advanced concepts, which is what serious students need today
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Table of contents (6 chapters)
Keywords
About this book
The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained.
The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
Reviews
“The present book is a very solid, and different than usual (or traditional), introduction to algebraic geometry that we can find on the market. … I can honestly recommend this item as a main reference for (advanced) courses devoted to algebraic geometry, and for extended courses devoted to introduction to algebraic geometry – this claim is based on the fact that the book is self-contained on the level of commutative algebra and due to this reason provides a coherent narration.” (Piotr Pokora, zbMATH 1471.14003, 2021)
Authors and Affiliations
About the authors
Sophie Kriz is Honors math major, LSA, at the University of Michigan in Ann Arbor, MI, USA
Bibliographic Information
Book Title: Introduction to Algebraic Geometry
Authors: Igor Kriz, Sophie Kriz
DOI: https://doi.org/10.1007/978-3-030-62644-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-62643-3Published: 14 March 2021
eBook ISBN: 978-3-030-62644-0Published: 13 March 2021
Edition Number: 1
Number of Pages: XIX, 470
Number of Illustrations: 347 b/w illustrations, 2 illustrations in colour
Topics: Algebraic Geometry