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Elementary Algebraic Geometry

Klaus Hulek Universität Hannover, Hannover, Germany
Available Formats:
Softcover ISBN: 978-0-8218-2952-3
Product Code: STML/20
List Price: $44.00 Individual Price:$35.20
Electronic ISBN: 978-1-4704-2134-2
Product Code: STML/20.E
List Price: $41.00 Individual Price:$32.80
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List Price: $66.00 Click above image for expanded view Elementary Algebraic Geometry Klaus Hulek Universität Hannover, Hannover, Germany Available Formats:  Softcover ISBN: 978-0-8218-2952-3 Product Code: STML/20  List Price:$44.00 Individual Price: $35.20  Electronic ISBN: 978-1-4704-2134-2 Product Code: STML/20.E  List Price:$41.00 Individual Price: $32.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$66.00
• Book Details

Student Mathematical Library
Volume: 202003; 213 pp
MSC: Primary 14;

This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra.

The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.

The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

Advanced undergraduates, graduate students, and research mathematicians interested in algebra and algebraic geometry; those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

• Chapters
• Chapter 0. Introduction
• Chapter 1. Affine varieties
• Chapter 2. Projective varieties
• Chapter 3. Smooth points and dimension
• Chapter 4. Plane cubic curves
• Chapter 5. Cubic surfaces
• Chapter 6. Introduction to the theory of curves

• Reviews

• The present small book offers a nice introduction to algebraic geometry, based on an elementary algebraic level, without the use of sheaf or cohomology theory. ...The book is nicely written and can be recommended to anybody interested in basic algebraic geometry.

• The book balances theory and examples well and the exercises are well-chosen to further illustrate the basic concepts. All in all, the book does an excellent job of explaining what algebraic geometry is about, what are the basic results, and it invites the reader to continue exploring the subject … I would definitely recommend it as reading material to a bright undergraduate who has taken a basic course on rings and fields and has read about Noetherian rings. It is certainly suitable for a one-semester graduate course … Mathematicians from other areas will also enjoy the book … [It] reminds me of more old-fashioned books on algebraic geometry … but updated to our modern standards of rigor and shorter attention span.

MAA Online
• From a review for the German Edition:

The introduction contains numerous examples which illustrate and motivate the discussed theory and which reappear, as the course develops, handled in a precise and clear manner … Each section ends with interesting and doable (!) exercises … the author makes a great effort to prove most of the theorems in the rigorous way … Precision and clarity are distinguished features of the reviewed test.

MathSciNet, Mathematical Reviews on the Web
• The book remains one of the very best introductory texts on algebraic geometry. The last chapter is a masterpiece of didactic art ... absolutely unique for such an elementary textbook.

Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 202003; 213 pp
MSC: Primary 14;

This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra.

The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.

The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

Advanced undergraduates, graduate students, and research mathematicians interested in algebra and algebraic geometry; those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

• Chapters
• Chapter 0. Introduction
• Chapter 1. Affine varieties
• Chapter 2. Projective varieties
• Chapter 3. Smooth points and dimension
• Chapter 4. Plane cubic curves
• Chapter 5. Cubic surfaces
• Chapter 6. Introduction to the theory of curves
• The present small book offers a nice introduction to algebraic geometry, based on an elementary algebraic level, without the use of sheaf or cohomology theory. ...The book is nicely written and can be recommended to anybody interested in basic algebraic geometry.

• The book balances theory and examples well and the exercises are well-chosen to further illustrate the basic concepts. All in all, the book does an excellent job of explaining what algebraic geometry is about, what are the basic results, and it invites the reader to continue exploring the subject … I would definitely recommend it as reading material to a bright undergraduate who has taken a basic course on rings and fields and has read about Noetherian rings. It is certainly suitable for a one-semester graduate course … Mathematicians from other areas will also enjoy the book … [It] reminds me of more old-fashioned books on algebraic geometry … but updated to our modern standards of rigor and shorter attention span.

MAA Online
• From a review for the German Edition:

The introduction contains numerous examples which illustrate and motivate the discussed theory and which reappear, as the course develops, handled in a precise and clear manner … Each section ends with interesting and doable (!) exercises … the author makes a great effort to prove most of the theorems in the rigorous way … Precision and clarity are distinguished features of the reviewed test.

MathSciNet, Mathematical Reviews on the Web
• The book remains one of the very best introductory texts on algebraic geometry. The last chapter is a masterpiece of didactic art ... absolutely unique for such an elementary textbook.

Zentralblatt MATH
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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