Overview
Compact exposition: Self contained introduction to algebraic curves in 5 chapters, complete exposition of foundations from category theory in 3 chapters and modern algebraic geometry in 14 chapters
Detailed exposition: Proofs, or the essential parts of proofs, are included for all major theorems given
Numerous illustrations
Includes supplementary material: sn.pub/extras
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Table of contents (22 chapters)
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Front Matter
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Introduction to Grothendieck’s Theory of Schemes
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Front Matter
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Introduction to Grothendieck's Theory of Schemes
Keywords
About this book
This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: “There is no royal road to geometry!”
The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royal road to algebraic geometry.
From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck’s theory of schemes. Contemporary homological tools are explained.
The reader will follow a directed path leading up to the main elements of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest scientific experience of a lifetime!
Reviews
From the reviews:
“The book sets out on a project to convey the big ideas of algebraic geometry in the 21st century in a way that will be accessible and that will get to get to the big ideas (relatively) quickly. … The topics … give a good overview of modern algebraic geometry, and I think that a reader who is interested in getting quick statements of theorems will find a lot to like in this book.” (Darren Glass, The Mathematical Association of America, August, 2012)
“The book under review offers a first introduction to algebraic geometry of a special kind … . quite a variety of topics from modern algebraic geometry is presented to the reader, often in a sketchy or survey-like manner, but always with hints for further reading. The sections of the single chapters are mostly short, and the presentation is nowhere lengthy or tedious. … the book must be seen as a charming invitation to algebraic geometry, along some sort of ‘royal road’ (of pleasure and diversity).” (Werner Kleinert, Zentralblatt MATH, Vol. 1237, 2012)
Authors and Affiliations
Bibliographic Information
Book Title: A Royal Road to Algebraic Geometry
Authors: Audun Holme
DOI: https://doi.org/10.1007/978-3-642-19225-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Hardcover ISBN: 978-3-642-19224-1Published: 06 October 2011
Softcover ISBN: 978-3-642-42921-7Published: 29 November 2013
eBook ISBN: 978-3-642-19225-8Published: 06 October 2011
Edition Number: 1
Number of Pages: XIV, 366
Topics: Algebraic Geometry, Category Theory, Homological Algebra, Geometry, Algebraic Topology, Commutative Rings and Algebras, History of Mathematical Sciences