Shafarevich Basic Algebraic Geometry 1

2. Auflage 1994
ISBN: 978-3-642-57908-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 304 Seiten, eBook

The first edition of this book came out just as the apparatus of algebraic geometry was reaching a stage that permitted a lucid and concise account of the foundations of the subject. The author was no longer forced into the painful choice between sacrificing rigour of exposition or overloading the clear geometrical picture with cumbersome algebraic apparatus. The 15 years that have elapsed since the first edition have seen the appear ance of many beautiful books treating various branches of algebraic geometry. However, as far as I know, no other author has been attracted to the aim which this book set itself: to give an overall view of the many varied aspects of algebraic geometry, without going too far afield into the different theories. There is thus scope for a second edition. In preparing this, I have included some additional material, rather varied in nature, and have made some small cuts, but the general character of the book remains unchanged.

Zielgruppe

Graduate

Autoren/Hrsg.

Shafarevich, Igor R.

Weitere Mitwirkende

Reid, M.

Inhaltsverzeichnis

I. Basic Notions.- 1. Algebraic Curves in the Plane.- Exercises to §1.- 2. Closed Subsets of Affine Space.- Exercises to §2.- 3. Rational Functions.- Exercises to §3.- 4. Quasiprojective Varieties.- Exercises to §4.- 5. Products and Maps of Quasiprojective Varieties.- Exercises to §5.- 6. Dimension.- Exercises to §6.- II. Local Properties.- 1. Singular and Nonsingular Points.- Exercises to §1.- 2. Power Series Expansions.- Exercises to §2.- Exercises to §3.- 4. The Structure of Birational Maps.- Exercises to §4.- 5. Normal Varieties.- Exercises to §5.- 6. Singularities of a Map.- Exercises to §6.- III. Divisors and Differential Forms.- 1. Divisors.- Exercises to §1.- 2. Divisors on Curves.- Exercises to §2.- 3. The Plane Cubic.- Exercises to §3.- 4. Algebraic Groups.- Exercises to §4.- 5. Differential Forms.- Exercises to §5.- 6. Examples and Applications of Differential Forms.- Exercises to §6.- IV. Intersection Numbers.- 1. Definition and Basic Properties.- Exercises to §1.- 2. Applications of Intersection Numbers.- Exercises to §2.- 3. Birational Maps of Surfaces.- Exercises to §3.- 4. Singularities.- Exercises to §4.- Algebraic Appendx.- References.