Classical Algebraic Geometry : A Modern View
Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
- Electronic book text
- 11 Sep 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 40 b/w illus. 25 tables 220 exercises
Table of contents
Preface; 1. Polarity; 2. Conics and quadrics; 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; Bibliography; Index.
'... the author has rendered a great, truly invaluable service to the community of algebraic geometers worldwide. No doubt, this great book is a product of ultimate enthusiasm, ethical principles and expertise, which will help preserve the precious legacy of classical algebraic geometry for further generations of researchers, teachers and students in the field.' Werner Kleinert, EMS Newsletter 'The amount of material covered is absolutely impressive - it reflects the amazing culture of the author ... [He] has rendered a great service to the algebraic geometry community: most of the material treated was available previously only in classical texts, which are quite difficult to read for modern mathematicians. This is a wonderful book. Anyone interested in classical algebraic geometry should have a copy.' Arnaud Beauville, Mathematical Reviews
About Igor V. Dolgachev
Igor V. Dolgachev is Professor Emeritus in the Department of Mathematics at the University of Michigan.