Lectures on Curves on an Algebraic Surface. (AM-59) ( Annals of Mathematics Studies )

Publication series ：Annals of Mathematics Studies

Author： Mumford David  

Publisher： Princeton University Press‎

Publication year： 2016

E-ISBN: 9781400882069

P-ISBN(Paperback): 9780691079936

Subject： O187.1 algebraic curve, algebraic surface

Keyword： 几何、拓扑,数学

Language： ENG

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Description

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 Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.

Chapter

Cover

Title

Copyright

Dedication

CONTENTS

INTRODUCTION

1: Raw Material on Curves on Surfaces, and the Problems Suggested

2: The Fundamental Existence Problem and Two Analytic Proofs

3: Pre-schemes and their Associated "Functor of Points"

4: Uses of the Functor of Points

Appendix to Lecture 4: Re Representable Functors and Zariski Tangent Spaces

5: Proj and Invertible Sheaves

6: Properties of Morphisms and Sheaves

7: Resume of the Cohomology of Coherent Sheaves on Pn

8: Flattening Stratifications

9: Cartier Divisors

10: Functorial Properties of Effective Cartier Divisors

11: Back to the Classical Case

12: The Over-all Classification of Curves on Surfaces

13: Linear Systems and Examples

14: Some Vanishing Theorems

15: Universal Families of Curves

16: The Method of Chow Schemes

17: Good Curves

18: The Index Theorem

19: The Picard Scheme: Outline

20: Independent 0-cycles on a Surface

21: The Picard Scheme: Conclusion

22: The Characteristic Map of a Family of Curves

23: The Fundamental Theorem V ia Kodaira-Spencer

24: The Structure of ϕ

25: The Fundamental Theorem Via Grothendieck-Cartier

26: Ring Schemes: The Witt Scheme

Appendix to Lecture 26:

27: The Fundamental Theorem in Characteristic p

BIBLIOGRAPHY

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