代数幾何：古典から現代へ Classical Algebraic Geometry : A Modern View

Dolgachev, Igor V.

Cambridge University Press（2012/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 652 p.／サイズ 40 b/w illus.
• 言語 ENG
• 商品コード 9781107017658
• DDC分類 516.35

基本説明

This detailed exposition makes the rich legacy of classical algebraic geometry accessible to modern algebraic geometers and to others who are interested in applying classical results.

Full Description

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

Contents

Preface; 1. Polarity; 2. Conics and quadrics; 3. Plane cubics; 4. Determinantal equations; 5. Theta characteristics; 6. Plane quartics; 7. Cremona transformations; 8. Del Pezzo surfaces; 9. Cubic surfaces; 10. Geometry of lines; Bibliography; Index.