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Algebraic Geometry 1: From Algebraic Varieties to Schemes
 
Kenji Ueno Kyoto University, Kyoto, Japan
Algebraic Geometry 1
Softcover ISBN:  978-0-8218-0862-7
Product Code:  MMONO/185
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-1-4704-4599-7
Product Code:  MMONO/185.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-0862-7
eBook: ISBN:  978-1-4704-4599-7
Product Code:  MMONO/185.B
List Price: $101.00 $76.50
MAA Member Price: $90.90 $68.85
AMS Member Price: $80.80 $61.20
Algebraic Geometry 1
Click above image for expanded view
Algebraic Geometry 1: From Algebraic Varieties to Schemes
Kenji Ueno Kyoto University, Kyoto, Japan
Softcover ISBN:  978-0-8218-0862-7
Product Code:  MMONO/185
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-1-4704-4599-7
Product Code:  MMONO/185.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-0862-7
eBook ISBN:  978-1-4704-4599-7
Product Code:  MMONO/185.B
List Price: $101.00 $76.50
MAA Member Price: $90.90 $68.85
AMS Member Price: $80.80 $61.20
  • Book Details
     
     
    Translations of Mathematical Monographs
    Iwanami Series in Modern Mathematics
    Volume: 1851999; 154 pp
    MSC: Primary 14;

    This is the first of three volumes on algebraic geometry. The second volume, Algebraic Geometry 2: Sheaves and Cohomology, is available from the AMS as Volume 197 in the Translations of Mathematical Monographs series.

    Early in the 20th century, algebraic geometry underwent a significant overhaul, as mathematicians, notably Zariski, introduced a much stronger emphasis on algebra and rigor into the subject. This was followed by another fundamental change in the 1960s with Grothendieck's introduction of schemes. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject.

    The book begins with a description of the standard theory of algebraic varieties. Then, sheaves are introduced and studied, using as few prerequisites as possible. Once sheaf theory has been well understood, the next step is to see that an affine scheme can be defined in terms of a sheaf over the prime spectrum of a ring. By studying algebraic varieties over a field, Ueno demonstrates how the notion of schemes is necessary in algebraic geometry.

    This first volume gives a definition of schemes and describes some of their elementary properties. It is then possible, with only a little additional work, to discover their usefulness. Further properties of schemes will be discussed in the second volume.

    Ueno's book is a self-contained introduction to this important circle of ideas, assuming only a knowledge of basic notions from abstract algebra (such as prime ideals). It is suitable as a text for an introductory course on algebraic geometry.

    Readership

    Undergraduates and first-year graduate students seeking an introduction to algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • Algebraic varieties
    • Schemes
    • Categories and schemes
  • Additional Material
     
     
  • Reviews
     
     
    • This treatise may serve as a first introduction for any student interested in algebraic geometry in the style of Grothendieck. It provides basic concepts and definitions, even introducing such notions as localizations, tensor products and inductive and projective limits. The material is illustrated by examples and figures, and some exercises provide the option to verify one's progress.

      Mathematical Reviews
    • This masterly written text, now also available to the international mathematical audience, tells its own tale and represents a highly welcome addition to the great standard textbooks on algebraic geometry.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 1851999; 154 pp
MSC: Primary 14;

This is the first of three volumes on algebraic geometry. The second volume, Algebraic Geometry 2: Sheaves and Cohomology, is available from the AMS as Volume 197 in the Translations of Mathematical Monographs series.

Early in the 20th century, algebraic geometry underwent a significant overhaul, as mathematicians, notably Zariski, introduced a much stronger emphasis on algebra and rigor into the subject. This was followed by another fundamental change in the 1960s with Grothendieck's introduction of schemes. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject.

The book begins with a description of the standard theory of algebraic varieties. Then, sheaves are introduced and studied, using as few prerequisites as possible. Once sheaf theory has been well understood, the next step is to see that an affine scheme can be defined in terms of a sheaf over the prime spectrum of a ring. By studying algebraic varieties over a field, Ueno demonstrates how the notion of schemes is necessary in algebraic geometry.

This first volume gives a definition of schemes and describes some of their elementary properties. It is then possible, with only a little additional work, to discover their usefulness. Further properties of schemes will be discussed in the second volume.

Ueno's book is a self-contained introduction to this important circle of ideas, assuming only a knowledge of basic notions from abstract algebra (such as prime ideals). It is suitable as a text for an introductory course on algebraic geometry.

Readership

Undergraduates and first-year graduate students seeking an introduction to algebraic geometry.

  • Chapters
  • Algebraic varieties
  • Schemes
  • Categories and schemes
  • This treatise may serve as a first introduction for any student interested in algebraic geometry in the style of Grothendieck. It provides basic concepts and definitions, even introducing such notions as localizations, tensor products and inductive and projective limits. The material is illustrated by examples and figures, and some exercises provide the option to verify one's progress.

    Mathematical Reviews
  • This masterly written text, now also available to the international mathematical audience, tells its own tale and represents a highly welcome addition to the great standard textbooks on algebraic geometry.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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