Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 /

Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 / / David Mumford.

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendiec...

Full description

Saved in:
Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Mumford, David,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1966
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 59
Online Access:
Physical Description:1 online resource (212 p.)
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Frontmatter
  • INTRODUCTION
  • CONTENTS
  • LECTURE 1. RAW MATERIAL ON CURVES ON SURFACES, AND THE PROBLEMS SUGGESTED
  • LECTURE 2. THE FUNDAMENTAL EXISTENCE PROBLEM AND TWO ANALYTIC PROOFS
  • LECTURE 3. PRE-SCHEMES AND THEIR ASSOCIATED "FUNCTOR OF POINTS"
  • LECTURE 4. USES OF THE FUNCTOR OF POINTS
  • APPENDIX TO LECTURE 4. RE REPRESENTABLE FUNCTORS AND ZARISKI TANGENT SPACES
  • LECTURE 5. Pro j AND INVERTIBLE SHEAVES
  • APPENDIX TO LECTURE 5
  • LECTURE 6. PROPERTIES OP MORPHISMS AND SHEAVES
  • LECTURE 7. RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON Pn
  • LECTURE 8. FLATTENING STRATIFICATIONS
  • LECTURE 9. CARTIER DIVISORS
  • LECTURE 10. FUNCTORIAL PROPERTIES OF EFFECTIVE CARTIER DIVISORS
  • LECTURE 11. BACK TO THE CLASSICAL CASE
  • LECTURE 12. THE OVER-ALL CLASSIFICATION OF CURVES ON SURFACES
  • LECTURE 13. LINEAR SYSTEMS AND EXAMPLES
  • LECTURE 14. SOME VANISHING THEOREMS
  • LECTURE 15. UNIVERSAL FAMILIES OF CURVES
  • LECTURE 16. THE METHOD OF CHOW SCHEMES
  • LECTURE 17. GOOD CURVES
  • LECTURE 18. THE INDEX THEOREM
  • LECTURE 19. THE PICARD SCHEME : OUTLINE
  • LECTURE 20. INDEPENDENT 0-CYCLES ON A SURFACE
  • LECTURE 21. THE PICARD SCHEME: CONCLUSION
  • LECTURE 22. THE CHARACTERISTIC MAP OP A FAMILY OP CURVES
  • LECTURE 23. THE FUNDAMENTAL THEOREM VIA KODAIRA-SPENCER
  • LECTURE 24. THE STRUCTURE OF Φ
  • LECTURE 25. THE FUNDAMENTAL THEOREM VIA GROTHENDIECK-CARTIER
  • LECTURE 26. RING SCHEMES; THE WITT SCHEME
  • APPENDICES TO LECTURE 26 APPENDICES TO LECTURE 26
  • LECTURE 27. THE FUNDAMENTAL THEOREM IN CHARACTERISTIC p
  • WORKS REFERRED TO
  • Backmatter

Similar Items