Red Book of Varieties and Schemes Includes the Michigan Lectures (1974) on Curves and Their Jacobians
Edition: 2nd 1999 (Revised)
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Description: Mumford's famous Red Bookgives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about. This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learn i) the concept of "scheme" as part of their study of algebraic geometry and ii) an overview of moduli problems for curves and of the use of theta functions to study these.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $74.95
Copyright year: 1999
Publication date: 9/17/1999
Size: 5.75" wide x 8.75" long x 0.75" tall
|Preface to the Second Edition|
|Preface to the First Edition|
|Irreducible algebraic sets|
|Definition of a morphism|
|Sheaves and affi ne varieties|
|Definition of prevarieties and morphisms|
|Products and the Hausdorff Axiom|
|The fibres of a morphism|
|The category of preschemes|
|Varieties and preschemes|
|Fields of definition|
|The functor of points of a prescheme|
|Proper morphisms and finite morphisms|
|Local Properties of Schemes|
|Non-singularity and differentials|
|Non-singularity and the UFD property|
|Normal varieties and normalization|
|Zariski's Main Theorem|
|Flat and smooth morphisms|
|Appendix: Curves and Their Jacobians|
|What is a Curve and How Explicitly Can We Describe Them?|
|The Moduli Space of Curves: Definition, Coordinatization, and Some Properties|
|How Jacobians and Theta Functions Arise|
|The Torelli Theorem and the Schottky Problem|
|Survey of Work on the Schottky Problem up to 1996 by Enrico Arbarello|
|References: The Red Book of Varieties and Schemes|
|Guide to the Literature and References: Curves and Their Jacobians|
|Supplementary Bibliography on the Schottky Problem by Enrico Arbarello|