Methods of algebraic geometry

著者

• Hodge, W. V. D. (William Vallance Douglas)
• Pedoe, Daniel

書誌事項

Methods of algebraic geometry

by W.V.D. Hodge and D. Pedoe

（Cambridge mathematical library）

Cambridge University Press, 1994

• 1 : pbk
• 2 : pbk
• 3 : pbk

注記

Includes bibliographies and index

v. 1: "First published 1947, Reprinted 1953, 1968, First paperback ed. 1968, Reissued in the Cambridge Mathematical Library 1994"--T.p. verso

v. 2: "First published 1952, Reprinted 1968 ..."--T.p. verso

v. 3: "First published 1954 ..."--T.p. verso

収録内容

• v. 1. book 1. Algebraic preliminaries. book 2. Projective space
• v. 2. book 3. General theory of algebraic varieties in projective space. book 4. Quadrics and Grassmann varieties
• v. 3. book 5. Birational geometry

内容説明・目次

巻冊次

3 : pbk ISBN 9780521467759

内容説明

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.

目次

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

巻冊次

1 : pbk ISBN 9780521469005

内容説明

This work provides a lucid and rigorous account of the foundations of modern 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. This first volume is divided into two parts. The first is devoted to pure algebra; the basic notions, the theory of matrices over a non-commutative ground field and a study of algebraic equations. The second part is concerned with the definitions and basic properties of projective space in n dimensions. It concludes with a purely algebraic account of collineations and correlations. 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.

目次

• Book I. Algebraic Preliminaries: 1. Rings and fields
• 2. Linear algebra, matrices, determinants
• 3. Algebraic dependence
• 4. Algebraic equations
• Book II. Projective Space: 5. Projective space: algebraic definition
• 6. Projective space: synthetic definition
• 7. Grassmann coordinates
• 8. Collineations
• 9. Correlations.

巻冊次

2 : pbk ISBN 9780521469012

内容説明

This work provides a lucid and rigorous account of the foundations of modern 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. Volume 2 gives an account of the principal methods used in developing a theory of algebraic varieties in spaces of n dimensions. Applications of these methods are also given to some of the more important varieties which occur in projective geometry. The ground field is without characteristic. Since geometry over any field without characteristic conforms to the general pattern of geometry over the field of complex numbers, a sound algebraic basis for classical geometry is provided. 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.

目次

• Part I. Book 3: General Theory of Algebraic Varieties in Projective Space
• 10. Algebraic varieties
• 11. Algebraic correspondences
• 12. Intersection theory
• Part II. Book 4: Quadrics and Grassmann Varieties
• 13. Quadrics
• 14. Grassmann varieties.

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詳細情報

• NII書誌ID(NCID): BA22320315
• ISBN:
  • 0521469007
  • 0521469015
  • 0521467756
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: 3 v.
• 大きさ: 23 cm
• 分類:
  • LCC : QA564
  • DC20 : 516.3/5
• 件名:
  • LCSH : Geometry, Algebraic
• 親書誌ID:
  • BA0151012X