Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarized higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes sketched in when the details are not essential for understanding the key ideas.
Author(s): Takao Fujita
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1990
Language: English
Pages: 219
Contents......Page 5
Introduction......Page 7
Acknowledgements......Page 12
1. Relative viewpoint......Page 15
2. Singularities......Page 20
3. Intersection theories......Page 23
4. Semipositive line bundles and vanishing theorems......Page 28
5. Birational classification of algebraic varieties......Page 33
1. Characterizations of projective spaces......Page 36
2. Basic notions in the Apollonius method......Page 39
3. Iteration of the Apollonius method......Page 42
4. Existence of a ladder......Page 45
5. Classification of polarized varieties of d-genus zero......Page 52
6. Polarized varieties of d-genus one: First step......Page 57
7. Results of Lefschetz type......Page 69
8. Classification of Del Pezzo manifolds......Page 76
9. Polarized varieties of d-genus one: remaining cases......Page 91
10. Polarized manifolds of d-genus two......Page 97
11. Semipositivity of adjoint bundles......Page 107
12. Polarized manifolds of sectional genus s 1......Page 121
13. Classification of polarized manifolds of a fixed sectional genus: higher dimensional cases......Page 122
14. Classification of polarized surfaces of a fixed sectional genus......Page 128
15. Polarized manifolds of sectional genus two......Page 136
16. Castelnuovo bounds......Page 153
17. Varieties of small degrees......Page 161
18. Adjunction theories......Page 165
19. Singular and quasi- polarized varieties......Page 178
20. Ample vector bundles......Page 185
21. Computer-aided enumeration of ruled polarized surfaces of a fixed sectional genus......Page 190
References......Page 198
Subject Index......Page 216
