Classical Algebraic Geometry A Modern View by Igor Dolgachev
Book Contents :-
1. Polarity page
2. Conics and quadric surfaces
3. Plane cubics
4. Determinantal equations
5. Theta characteristics
6. Plane Quartics
7. Cremona transformations
8. Del Pezzo surfaces
9. Cubic surfaces
10. Geometry of Lines
About this book :-
"Classical Algebraic Geometry" by Igor V. Dolgachev is a well-known graduate-level book that revisits "classical algebraic geometry" using the language and tools of modern mathematics. The book focuses on the geometry of algebraic varieties in projective space and explains how many classical results can be understood more clearly through modern concepts. It is written for readers who already have some background in algebraic geometry.
The text covers important topics such as "projective geometry", plane algebraic curves, cubic and quartic surfaces, Cremona transformations, and the geometry of lines and surfaces. One of the book’s strengths is how it connects historical results with modern theory, allowing readers to see both the origins and the current relevance of the subject. The exposition is careful and detailed, making difficult ideas easier to follow for serious students.
Overall, this book serves as both a reference and a learning resource for advanced readers interested in "algebraic varieties" and their geometric properties. With a large number of exercises and references, it is especially useful for graduate students and researchers who want a deeper understanding of "modern techniques" applied to classical problems in algebraic geometry.
Book Detail :-
Title:
Classical Algebraic Geometry A Modern View by Igor Dolgachev
Publisher:
Cambridge University Press
Year:
2012
Pages:
722
Type:
PDF
Language:
English
ISBN-10 #:
1107017653
ISBN-13 #:
978-3642725494
License:
External Educational Resource
Amazon:
Amazon
About Author :-
The author
Igor V. Dolgachev
(born 1944) is a well-known Russian–American mathematician recognized for his influential work in "algebraic geometry". His research focuses on "projective geometry", algebraic surfaces, and invariant theory, where he bridges classical geometric ideas with modern mathematical techniques. He is respected for presenting complex concepts with clarity and strong geometric intuition. Dolgachev has been a long-time professor at the "University of Michigan", contributing significantly to academic research and graduate education. As an author, he is admired for writing advanced yet accessible texts. His work remains highly relevant for researchers studying "classical geometry" through a modern lens and continues to shape developments in "mathematical research".
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