A Royal Road to Algebraic Geometry

  • Audun Holme

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Curves

    1. Front Matter
      Pages 1-1
    2. Audun Holme
      Pages 3-12
    3. Audun Holme
      Pages 39-62
    4. Audun Holme
      Pages 63-118
  3. Introduction to Grothendieck’s Theory of Schemes

    1. Front Matter
      Pages 141-141
    2. Audun Holme
      Pages 143-160
    3. Audun Holme
      Pages 161-164
    4. Audun Holme
      Pages 165-183
    5. Audun Holme
      Pages 185-194
    6. Audun Holme
      Pages 195-215
    7. Audun Holme
      Pages 217-238
    8. Audun Holme
      Pages 239-245
    9. Audun Holme
      Pages 253-261
    10. Audun Holme
      Pages 263-274
    11. Audun Holme
      Pages 275-284
    12. Audun Holme
      Pages 285-305
    13. Audun Holme
      Pages 307-319
    14. Audun Holme
      Pages 329-334
    15. Audun Holme
      Pages 343-355
  4. Back Matter
    Pages 357-364

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!


Algebraic curves Algebraic geometry Category theory Homological algebra

Authors and affiliations

  • Audun Holme
    • 1
  1. 1.Department of MathematicsUniversity of BergenBergenNorway

Bibliographic information