Student Mathematical Library
Volume: 20;
2003;
213 pp;
Softcover
MSC: Primary 14;
Print ISBN: 978-0-8218-2952-3
Product Code: STML/20
List Price: $41.00
Individual Price: $32.80
Electronic ISBN: 978-1-4704-2134-2
Product Code: STML/20.E
List Price: $41.00
Individual Price: $32.80
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Supplemental Materials
Elementary Algebraic Geometry
Share this pageKlaus Hulek
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.
Readership
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.
Reviews & Endorsements
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.
-- EMS Newsletter
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
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
Table of Contents
Table of Contents
Elementary Algebraic Geometry
- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Chapter 0. Introduction 110 free
- Exercises 1524 free
- Chapter 1. Affine Varieties 1726
- Chapter 2. Projective Varieties 6372
- Chapter 3. Smooth Points and Dimension 97106
- Chapter 4. Plane Cubic Curves 115124
- Chapter 5. Cubic Surfaces 143152
- Chapter 6. Introduction to the Theory of Curves 167176
- Bibliography 207216
- Index 211220
- Back Cover Back Cover1225