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