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A Royal Road to Algebraic Geometry

Authors: Holme, Audun

  • 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
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eBook $54.99
price for USA
  • ISBN 978-3-642-19225-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Hardcover $74.95
price for USA
  • ISBN 978-3-642-19224-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-3-642-42921-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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)


Table of contents (22 chapters)

Buy this book

eBook $54.99
price for USA
  • ISBN 978-3-642-19225-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Hardcover $74.95
price for USA
  • ISBN 978-3-642-19224-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-3-642-42921-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Royal Road to Algebraic Geometry
Authors
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-19225-8
DOI
10.1007/978-3-642-19225-8
Hardcover ISBN
978-3-642-19224-1
Softcover ISBN
978-3-642-42921-7
Edition Number
1
Number of Pages
XIV, 366
Topics