| 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. |
| book 1. varieties in projective space chapter i. basic notions 1. algebraic curves in the plane 1.1. plane curves 1.2. rational curves 1.3. relation with field theory 1.4. rational maps 1.5. singular and nonsingular points 1.6. the projective plane exercises to 1 2. closed subsets of affine space 2.1. definition of closed subsets 2.2. regular functions on a closed subset 2.3. regular maps exercises to 2 3. rational functions 3.1. irreducible algebraic subsets 3.2. rational functions 3.3. rational maps exercises to 3 4 quasiprojectiove varieties 4.1 closied subsets of projectiive space 4.2 regular functions 4.3 rational functions 4.4 examples of regual maps exercises to 4 …… chapter ⅱ local properties chapter ⅲ divisors and differential forms chapter ⅳ intersection numbers algebraic appendix rererences index |
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