Homology theory on algebraic varieties

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
CONTENTS......Page 6
INTRODUCTION......Page 8
1. Hyperplane sections of a non-singular variety......Page 10
2. A family of linear sections of W......Page 11
3. The fibring of a variety defined over the complex numbers......Page 16
4. Homology groups related to V(K)......Page 26
1. Statement of the results......Page 32
2. Proof of Theorem 11......Page 34
1. The choice of a pencil......Page 43
2. Notation......Page 46
1. Lefschetz\'s first main theorem......Page 52
3. Sketch proof of Theorem 19......Page 58
4. Some immediate consequences......Page 63
1. Deformation theorems......Page 65
2. Some remarks dh Theorem 19......Page 69
3. Formal verification of Theorem 19; the vanishing cycle......Page 71
4. Proof of Theorem 19, parts (1) and (2)......Page 73
5. Proof of Theorem 19, part (3)......Page 76
1. The automorphisms T,......Page 81
2. Explicit calculation of T......Page 85
3. The formula .........Page 90
1. Clockwise and anti-clockwise isomorphisms......Page 92
2. A special representative for......Page 96
3. Proof of Theorem 32......Page 97
4. Proof of Theorem 34......Page 99
1. Summary of results assumed......Page 106
2. The intersection and locus operators......Page 107
3. Direct decomposition for H_{r-1}(V_0,P)......Page 110
4. Direct decomposition of H_{r-1}(V_0)......Page 111
5. Proofs of Theorems 41 and 42......Page 115
REFERENCES......Page 124