LECTURE 22. THE CHARACTERISTIC MAP OP A FAMILY OP CURVES

Kapitel in diesem Buch

1. Frontmatter i
2. INTRODUCTION vii
3. CONTENTS xi
4. LECTURE 1. RAW MATERIAL ON CURVES ON SURFACES, AND THE PROBLEMS SUGGESTED 1
5. LECTURE 2. THE FUNDAMENTAL EXISTENCE PROBLEM AND TWO ANALYTIC PROOFS 7
6. LECTURE 3. PRE-SCHEMES AND THEIR ASSOCIATED “FUNCTOR OF POINTS” 11
7. LECTURE 4. USES OF THE FUNCTOR OF POINTS 17
8. APPENDIX TO LECTURE 4. RE REPRESENTABLE FUNCTORS AND ZARISKI TANGENT SPACES 25
9. LECTURE 5. Pro j AND INVERTIBLE SHEAVES 27
10. APPENDIX TO LECTURE 5 35
11. LECTURE 6. PROPERTIES OP MORPHISMS AND SHEAVES 37
12. LECTURE 7. RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON P_n 47
13. LECTURE 8. FLATTENING STRATIFICATIONS 55
14. LECTURE 9. CARTIER DIVISORS 61
15. LECTURE 10. FUNCTORIAL PROPERTIES OF EFFECTIVE CARTIER DIVISORS 69
16. LECTURE 11. BACK TO THE CLASSICAL CASE 75
17. LECTURE 12. THE OVER-ALL CLASSIFICATION OF CURVES ON SURFACES 83
18. LECTURE 13. LINEAR SYSTEMS AND EXAMPLES 91
19. LECTURE 14. SOME VANISHING THEOREMS 99
20. LECTURE 15. UNIVERSAL FAMILIES OF CURVES 105
21. LECTURE 16. THE METHOD OF CHOW SCHEMES 111
22. LECTURE 17. GOOD CURVES 119
23. LECTURE 18. THE INDEX THEOREM 127
24. LECTURE 19. THE PICARD SCHEME : OUTLINE 133
25. LECTURE 20. INDEPENDENT 0-CYCLES ON A SURFACE 139
26. LECTURE 21. THE PICARD SCHEME: CONCLUSION 145
27. LECTURE 22. THE CHARACTERISTIC MAP OP A FAMILY OP CURVES 151
28. LECTURE 23. THE FUNDAMENTAL THEOREM VIA KODAIRA-SPENCER 157
29. LECTURE 24. THE STRUCTURE OF Φ 161
30. LECTURE 25. THE FUNDAMENTAL THEOREM VIA GROTHENDIECK-CARTIER 167
31. LECTURE 26. RING SCHEMES; THE WITT SCHEME 171
32. APPENDICES TO LECTURE 26 APPENDICES TO LECTURE 26 189
33. LECTURE 27. THE FUNDAMENTAL THEOREM IN CHARACTERISTIC p 193
34. WORKS REFERRED TO 199
35. Backmatter 204