Methods of Algebraic Geometry: Volume 3

All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

W. V. D. Hodge (Author), D. Pedoe (Author)

9780521467759, Cambridge University Press

Paperback, published 19 May 1994

348 pages
22.8 x 15.1 x 2 cm, 0.501 kg

'Motivations are given. Examples of significant and useful varieties are numerous. All the algebra needed is given, and, what is more, these books tell how to translate geometry into algebra, and conversely.' Bulletin of the American Mathematical Society

This work provides a lucid and rigorous account of the foundations of algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Here in this volume, the authors have again confined their attention to varieties defined on a ground field without characteristic. In order to familiarize the reader with the different techniques available to algebraic geometers, they have not confined themselves to one method and on occasion have deliberately used more advanced methods where elementary ones would serve, when by so doing it has been possible to illustrate the power of the more advanced techniques, such as valuation theory. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Part I. Book 5: Birational Geometry: 15. Ideal theory of commutative rings
16. The arithmetic theory of varieties
17. Valuation theory
18. Birational transformations.

Subject Areas: Algebraic geometry [PBMW]