Red Book of Varieties and Schemes Includes the Michigan Lectures (1974) on Curves and Their Jacobians

Name: Red Book of Varieties and Schemes Includes the Michigan Lectures (1974) on Curves and Their Jacobians
Price: 68.55 USD
Availability: InStock
ISBN: 9783540632931

ISBN-10: 354063293X

ISBN-13: 9783540632931

Edition: 2nd 1999 (Revised)

Authors: David B. Mumford, A. Dold, B. Eckmann, E. Arbarello

List price: $74.95

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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…

Book details

List price: $74.95
Edition: 2nd
Copyright year: 1999
Publisher: Springer
Publication date: 9/17/1999
Binding: Paperback
Pages: 314
Size: 5.75" wide x 8.75" long x 0.75" tall
Weight: 1.122
Language: English



Preface to the Second Edition


Preface to the First Edition



Varieties



Some algebra



Irreducible algebraic sets



Definition of a morphism



Sheaves and affi ne varieties



Definition of prevarieties and morphisms



Products and the Hausdorff Axiom



Dimension



The fibres of a morphism



Complete varieties



Complex varieties



Preschemes



Spec (R)



The category of preschemes



Varieties and preschemes



Fields of definition



Closed subpreschemes



The functor of points of a prescheme



Proper morphisms and finite morphisms



Specialization



Local Properties of Schemes



Quasi-coherent modules



Coherent modules



Tangent cones



Non-singularity and differentials



ï¿½tale morphisms



Uniformizing parameters



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