Elementary Algebraic Geometry: Second Edition
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator.
An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring theory and algebraic geometry as well as varieties of arbitrary dimension and some elementary mathematics on curves. Upon finishing the text, students will have a foundation for advancing in several different directions, including toward a further study of complex algebraic or analytic varieties or to the scheme-theoretic treatments of algebraic geometry.
2015 edition.
1029867997
Elementary Algebraic Geometry: Second Edition
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator.
An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring theory and algebraic geometry as well as varieties of arbitrary dimension and some elementary mathematics on curves. Upon finishing the text, students will have a foundation for advancing in several different directions, including toward a further study of complex algebraic or analytic varieties or to the scheme-theoretic treatments of algebraic geometry.
2015 edition.
22.95 In Stock
Elementary Algebraic Geometry: Second Edition

Elementary Algebraic Geometry: Second Edition

by Keith Kendig
Elementary Algebraic Geometry: Second Edition

Elementary Algebraic Geometry: Second Edition

by Keith Kendig

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Overview

Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator.
An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring theory and algebraic geometry as well as varieties of arbitrary dimension and some elementary mathematics on curves. Upon finishing the text, students will have a foundation for advancing in several different directions, including toward a further study of complex algebraic or analytic varieties or to the scheme-theoretic treatments of algebraic geometry.
2015 edition.

Product Details

ISBN-13: 9780486801872
Publisher: Dover Publications
Publication date: 12/19/2014
Series: Dover Books on Mathematics
Sold by: Barnes & Noble
Format: eBook
Pages: 320
File size: 36 MB
Note: This product may take a few minutes to download.

About the Author

Keith Kendig is Professor Emeritus of Mathematics at Cleveland State University. He is the author of several volumes in the Mathematical Association of America's Dolciani Mathematical Expositions series, including Conics, 2005 and Sink or Float: Thought Problems in Math and Physics.

Table of Contents

Chapter I Examples of curves 1

1 Introduction 1

2 The topology of a few specific plane curves 5

3 Intersecting curves 19

4 Curves over Q 25

Chapter II Plane curves 28

1 Projective spaces 28

2 Affine and projective varieties; examples 34

3 Implicit mapping theorems 46

4 Some local structure of plane curves 54

5 Sphere coverings 66

6 The dimension theorem for plane curves 75

7 A Jacobian criterion for nonsingularity 80

8 Curves in P2(C) are connected 86

9 Algebraic curves are orientable 93

10 The genus formula for nonsingular curves 97

Chapter III Commutative ring theory and algebraic geometry 103

1 Introduction 103

2 Some basic lattice-theoretic properties of varieties and ideals 106

3 The Hilbert basis theorem 117

4 Some basic decomposition theorems on ideals and varieties 121

5 The Nullstellensatz: Statement and consequences 124

6 Proof of the Nullstellensatz 128

7 Quotient rings and subvarieties 132

8 Isomorphic coordinate rings and varieties 136

9 Induced lattice properties of coordinate ring surjections; examples 143

10 Induced lattice properties of coordinate ring injections 150

11 Geometry of coordinate ring extensions 155

Chapter IV Varieties of arbitrary dimension 163

1 Introduction 163

2 Dimension of arbitrary varieties 165

3 The dimension theorem 181

4 A Jacobian criterion for nonsingularity 187

5 Connectedness and orientability 191

6 Multiplicity 193

7 Bezout's theorem 207

Chapter V Some elementary mathematics on curves 214

1 Introduction 214

2 Valuation rings 215

3 Local rings 235

4 A ring-theoretic characterization of nonsingularity 248

5 Ideal theory on a nonsingular curve 255

6 Some elementary function theory on a nonsingular curve 266

7 The Riemann-Roch theorem 279

Bibliography 297

Notation index 299

Subject index 301

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