Introduction to Algebraic Geometry 1st Edition by Justin Smith ISBN 1503381536 978-1503381537

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Product details: 

ISBN 10: 1503381536

ISBN 13:  978-1503381537

Author: Justin R. Smith
This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of point-set topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. It also presents applications to robotics and other fields.

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
 6.5. The Hurwitz-Riemann Formula
 6.6. The j-invariant

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Justin Smith,Algebraic Geometry