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The red book of varieties and schemes: : includes the Michigan Lectures (1974) on curves and their Jacobians/ David Mumford

By: Mumford, DavidSeries: (Lecture notes in mathematics) ; 1358Publication details: Berlin: Springer, 1999Edition: 2nd expanded edDescription: x, 304 p. : ill. ; 24 cmISBN: 354063293XSubject(s): Algebraic Geometry | MathematicsDDC classification: 516.35

Contents:

I. Varieties -- 1. Some algebra -- 2. Irreducible algebraic sets -- 3. Definition of a morphism -- 4. Sheaves and affine varieties -- 5. Definition of prevarieties and morphisms -- 6. Products and the Hausdorff Axiom -- 7. Dimension -- 8. The fibres of a morphism -- 9. Complete varieties -- 10. Complex varieties -- II. Preschemes -- 1. Spec (R) -- 2. The category of preschemes -- 3. Varieties and preschemes -- 4. Fields of definition -- 5. Closed subpreschemes -- 6. The functor of points of a prescheme -- 7. Proper morphisms and finite morphisms -- 8. Specialization -- III. Local Properties of Schemes -- 1. Quasi-coherent modules -- 2. Coherent modules -- 3. Tangent cones -- 4. Non-singularity and differentials -- 5. Etale morphisms -- 6. Uniformizing parameters -- 7. Non-singularity and the UFD property -- 8. Normal varieties and normalization -- 9. Zariski's Main Theorem -- 10. Flat and smooth morphisms -- App. Curves and Their Jacobians -- Lecture I. What is a Curve and How Explicitly Can We Describe Them? -- Lecture II. The Moduli Space of Curves: Definition, Coordinatization, and Some Properties -- Lecture III. How Jacobians and Theta Functions Arise -- Lecture IV. The Torelli Theorem and the Schottky Problem -- Survey of Work on the Schottky Problem up to 1996 / 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 / Enrico Arbarello.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	516.35 MUM/R (Browse shelf(Opens below))	Available		49817

Total holds: 0

I. Varieties --
1. Some algebra --
2. Irreducible algebraic sets --
3. Definition of a morphism --
4. Sheaves and affine varieties --
5. Definition of prevarieties and morphisms --
6. Products and the Hausdorff Axiom --
7. Dimension --
8. The fibres of a morphism --
9. Complete varieties --
10. Complex varieties --
II. Preschemes --
1. Spec (R) --
2. The category of preschemes --
3. Varieties and preschemes --
4. Fields of definition --
5. Closed subpreschemes --
6. The functor of points of a prescheme --
7. Proper morphisms and finite morphisms --
8. Specialization --
III. Local Properties of Schemes --
1. Quasi-coherent modules --
2. Coherent modules --
3. Tangent cones --
4. Non-singularity and differentials --
5. Etale morphisms --
6. Uniformizing parameters --
7. Non-singularity and the UFD property --
8. Normal varieties and normalization --
9. Zariski's Main Theorem --
10. Flat and smooth morphisms --
App. Curves and Their Jacobians --
Lecture I. What is a Curve and How Explicitly Can We Describe Them? --
Lecture II. The Moduli Space of Curves: Definition, Coordinatization, and Some Properties --
Lecture III. How Jacobians and Theta Functions Arise --
Lecture IV. The Torelli Theorem and the Schottky Problem --
Survey of Work on the Schottky Problem up to 1996 / 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 / Enrico Arbarello.

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