Author(s): Andrew H Wallace
Series: International series of monographs on pure and applied mathematics
Edition: 1st
Publisher: Pergamon Press
Year: 1958
Language: English
Pages: 122
Cover......Page 1
Title Page......Page 2
Copyright......Page 3
CONTENTS ......Page 4
INTRODUCTION ......Page 6
1. Hyperplane sections of a non-singular variety ......Page 8
2. A family of linear sections of W ......Page 9
3. The fibring of a variety defined over the complex numbers ......Page 14
4. Homology groups related to V(K) ......Page 24
1. Statement of the results ......Page 30
2. Proof of Theorem 11 ......Page 32
1. The choice of a pencil ......Page 41
2. Notation ......Page 44
3. Reduction to local theorems 38. ......Page 0
1. Lefschetz's first main theorem ......Page 50
3. Sketch proof of Theorem 19 ......Page 56
.4. Some immediate consequences ......Page 91
1. Deformation theorems ......Page 63
2. Some remarks dh Theorem 19 ......Page 87
3. Formal verification of Theorem 19; the vanishing cycle ......Page 69
4. Proof of Theorem 19, parts (1) and (2) ......Page 71
2. A special representative for ......Page 94
1. The automorphisms T, ......Page 79
2. Explicit calculation of T ......Page 83
3. The formula T(y)* = y" - (y . b)$ ......Page 88
1. Clockwise and anti-clockwise isomorphisms ......Page 90
3. Proof of Theorem 32 ......Page 95
4. Proof of Theorem 34 ......Page 97
1. Summary of results assumed ......Page 104
2. The intersection and locus operators ......Page 105
3. Direct decomposition for H,_i(VO,P) ......Page 108
4. Direct decomposition of Hr-i(V0) ......Page 109
5. Proofs of Theorems 41 and 42 ......Page 113
REFERENCES ......Page 122
