Basic Algebraic Geometry

I.R. Shafarevich (Autor)

Buch | Softcover

XVI, 440 Seiten

1977 | 1st ed. 1974. Rev. 3rd printing
Springer Berlin (Verlag)
978-3-540-08264-4 (ISBN)

Infos

Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this do mam. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. Around 1910 Klein wrote: "When I was a student, Abelian functions -as an after-effect of Jacobi's tradition-were regarded as the undIsputed summit of mathe matics, and each of us, as a matter of course, had the ambition to forge ahead in this field. And now? The young generation hardly know what Abelian functions are." (Vorlesungen tiber die Entwicklung der Mathe matik im XIX. Jahrhundert, Springer-Verlag, Berlin 1926, Seite 312). The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axio matic spirit, which then determined the development of mathematics. Several decades had to lapse before the rise of the theory of topolo gical, differentiable and complex manifolds, the general theory of fields, the theory of ideals in sufficiently general rings, and only then it became possible to construct algebraic geometry on the basis of the principles of set-theoretical mathematics. Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics.

Inhalt

I. Algebraic Varieties in a Projective Space.- I. Fundamental Concepts.- II. Local Properties.- III. Divisors and Differential Forms.- IV. Intersection Indices.- II. Schemes and Varieties.- V. Schemes.- VI. Varieties.- III. Algebraic Varieties over the Field of Complex Numbers and Complex Analytic Manifolds.- VII. Topology of Algebraic Varieties.- VIII. Complex Analytic Manifolds.- IX. Uniformization.- Historical Sketch.- 1. Elliptic Integrals.- 2. Elliptic Functions.- 3. Abelian Integrals.- 4. Riemann Surfaces.- 5. The Inversion Problem.- 6. Geometry of Algebraic Curves.- 7. Many-Dimensional Geometry.- 8. The Analytic Theory of Manifolds.- 9. Algebraic Varieties over an Arbitrary Field. Schemes.- Bibliography for the Historical Sketch.- List of Notation.

Produkt-Details

• Erscheint lt. Verlag: 1.6.1977
• Reihe/Serie: Springer Study Edition
• Übersetzer: K.A. Hirsch
• Zusatzinfo: XVI, 440 p.
• Verlagsort: Berlin
• Sprache: englisch
• Maße: 155 x 235 mm
• Gewicht: 675 g
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Algebra • Algebraic • BASIC • Function • Geometry • manifold • Mathematics
• ISBN-10: 3-540-08264-6 / 3540082646
• ISBN-13: 978-3-540-08264-4 / 9783540082644
• Zustand: Neuware