Methods of algebraic geometry  1 ~ 3

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

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

[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.

「Nielsen BookData」より

[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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[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.

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この本の情報

書名 Methods of algebraic geometry
著作者等 Hodge, W. V. D.
Pedoe, Daniel
Pedoe Dan
Hodge W.V.D.
シリーズ名 Cambridge mathematical library
巻冊次 1
2
3
出版元 Cambridge University Press
刊行年月 1994
ページ数 3 v.
大きさ 23 cm
ISBN 0521467756
0521469015
0521469007
NCID BA22320315
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス

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