- 212 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Lectures on Curves on an Algebraic Surface
About this book
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.
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Yes, you can access Lectures on Curves on an Algebraic Surface by David Mumford in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebraic Geometry. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- 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
- 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
- 27: The Fundamental Theorem in Characteristic p
- BIBLIOGRAPHY