
Classical Algebraic Geometry: Volume 1
A Modern View
Igor V. Dolgachev(Author)
Cambridge University Press
2nd Edition
Will be published approx. on 31. July 2026
Book
Paperback/Softback
526 pages
978-1-009-73388-5 (ISBN)
Description
The 20th century saw the development of many of the key concepts and theories in algebraic geometry. However, the evolution of style and approach over time has rendered the original texts challenging for modern readers to decipher. Bridging the gap between classical and modern algebraic geometry, this book explains classical results using modern tools and language. The second edition has undergone significant expansion. This first volume includes an extensive look at the enumerative geometry of quadrics and a more in-depth exploration of Cremona transformations, featuring more examples of different types. Furthermore, the expanded bibliography now encompasses over 800 references, including references to results obtained in the twelve years since the publication of the first edition. This carefully crafted reference will continue to keep classical algebraic geometry results alive and accessible to new generations of graduate students and researchers today.
Reviews / Votes
'The first edition of this book has become the absolute reference for the treatment of classical algebraic geometry in modern terms. The new edition brings a series of important complements on most chapters, in particular on congruences of lines and quartic surfaces. In total this makes a very rich and complete book on the subject.' Arnaud Beauville, Professeur emerite, Universite Cote d'AzurMore details
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
ISBN-13
978-1-009-73388-5 (9781009733885)
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Schweitzer Classification
Person
Igor V. Dolgachev is Professor Emeritus at the University of Michigan. He has published over 100 research papers in various areas of algebraic geometry, and is the author of several books, including Lectures on Invariant Theory (2003) and Enriques Surfaces I & II (2025).
Content
Preface; Preface to the Second Edition; 1. Polarity; 2. Conics and Quadric Surfaces; 3. Plane Cubics; 4. Determinantal Varieties; 5. Theta Characteristics; 6. Plane Quartics; 7. Cremona Transformations.