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AuthorShafarevich, Igor R. author
TitleBasic Algebraic Geometry 1 [electronic resource] / by Igor R. Shafarevich
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994
Edition Second, Revised and Expanded Edition
Connect tohttp://dx.doi.org/10.1007/978-3-642-57908-0
Descript XX, 304 p. online resource

SUMMARY

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 appearยญ 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


CONTENT

I. Basic Notions -- 1. Algebraic Curves in the Plane -- Exercises to ยง1 -- 2. Closed Subsets of Affine Space -- Exercises to ยง2 -- 3. Rational Functions -- Exercises to ยง3 -- 4. Quasiprojective Varieties -- Exercises to ยง4 -- 5. Products and Maps of Quasiprojective Varieties -- Exercises to ยง5 -- 6. Dimension -- Exercises to ยง6 -- II. Local Properties -- 1. Singular and Nonsingular Points -- Exercises to ยง1 -- 2. Power Series Expansions -- Exercises to ยง2 -- Exercises to ยง3 -- 4. The Structure of Birational Maps -- Exercises to ยง4 -- 5. Normal Varieties -- Exercises to ยง5 -- 6. Singularities of a Map -- Exercises to ยง6 -- III. Divisors and Differential Forms -- 1. Divisors -- Exercises to ยง1 -- 2. Divisors on Curves -- Exercises to ยง2 -- 3. The Plane Cubic -- Exercises to ยง3 -- 4. Algebraic Groups -- Exercises to ยง4 -- 5. Differential Forms -- Exercises to ยง5 -- 6. Examples and Applications of Differential Forms -- Exercises to ยง6 -- IV. Intersection Numbers -- 1. Definition and Basic Properties -- Exercises to ยง1 -- 2. Applications of Intersection Numbers -- Exercises to ยง2 -- 3. Birational Maps of Surfaces -- Exercises to ยง3 -- 4. Singularities -- Exercises to ยง4 -- Algebraic Appendx -- References


Mathematics Algebraic geometry Physics Mathematics Algebraic Geometry Theoretical Mathematical and Computational Physics



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