(Ebook) Introduction to Algebraic Geometry 1st Edition by Justin R Smith ISBN 9781503381537 1503381536

(Ebook) Introduction to Algebraic Geometry 1st Edition by Justin R Smith ISBN 9781503381537 1503381536

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ISBN 10: 1503381536
ISBN 13: 9781503381537
Author: Justin R Smith

I am grateful to Patrick Clarke and Thomas Yu for many helpful and interesting discussions. Their insights and comments have improved this book considerably. I am also grateful to people at mathoverflow.net for their comments. The list includes (but is not limited to): Matthew Emerton, Will Swain, Nick Ramsey, and Angelo Vistoli.
I am indebted to Noel Robinson for pointing out a gap in the proof of corollary 2.8.30 on page 110. Correcting it entailed adding the material on uniform Krull dimension in section 2.8.2 on page 100.
I am also grateful to Matthias Ettrich and the many other developers of the software, LYX — a free front end to LATEX that has the ease of use of a word processor, with spell-checking, an excellent equation editor, and a thesaurus. I have used this software for years and the current version is more polished and bug-free than most commercial software.

(Ebook) Introduction to Algebraic Geometry 1st Edition Table of contents:

Chapter 1. A Classical Result
1.1. Bézout’s Theorem
1.2. The Projective Plane
1.3. The Sylvester Matrix
1.4. Application to Bézout’s Theorem
1.5. The Mystic Hexagram
1.6. Robotics

Chapter 2. Affine Varieties
2.1. Introduction
2.2. Hilbert’s Nullstellensatz
2.3. Computations in Polynomial Rings: Gröbner Bases
2.4. The Coordinate Ring
2.5. specm *
2.6. Applications to Optimization Theory
2.7. Products
2.8. Dimension

Chapter 3. Local Properties of Affine Varieties
3.1. Introduction
3.2. The Coordinate Ring at a Point
3.3. The Tangent Space
3.4. Normal Varieties and Finite Maps
3.5. Vector Bundles on Affine Varieties

Chapter 4. Varieties and Schemes
4.1. Introduction
4.2. Affine Schemes
4.3. Subschemes and Ringed Spaces
4.4. Schemes
4.5. Products
4.6. Varieties and Separated Schemes

Chapter 5. Projective Varieties
5.1. Introduction
5.2. Grassmannians
5.3. Invertible Sheaves on Projective Varieties
5.4. Regular and Rational Maps
5.5. Products
5.6. Noether Normalization
5.7. Graded Ideals and Modules
5.8. Bézout’s Theorem Revisited
5.9. Divisors

Chapter 6. Curves
6.1. Basic Properties
6.2. Elliptic Curves
6.3. The Riemann-Roch Theorem
6.4. The Modern Approach to Riemann-Roch

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Tags: Justin R Smith, Algebraic Geometry