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Introduction to Algebraic Geometry
 
Steven Dale Cutkosky University of Missouri, Columbia, MO
Introduction to Algebraic Geometry
Hardcover ISBN:  978-1-4704-3518-9
Product Code:  GSM/188
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-4670-3
Product Code:  GSM/188.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-3518-9
eBook: ISBN:  978-1-4704-4670-3
Product Code:  GSM/188.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Introduction to Algebraic Geometry
Click above image for expanded view
Introduction to Algebraic Geometry
Steven Dale Cutkosky University of Missouri, Columbia, MO
Hardcover ISBN:  978-1-4704-3518-9
Product Code:  GSM/188
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-4670-3
Product Code:  GSM/188.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-3518-9
eBook ISBN:  978-1-4704-4670-3
Product Code:  GSM/188.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1882018; 484 pp
    MSC: Primary 14

    This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic \(0\) and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters.

    With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

    Readership

    Graduate students and researchers interested in algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • A crash course in commutative algebra
    • Affine varieties
    • Projective varieties
    • Regular and rational maps of quasi-projective varieties
    • Products
    • The blow-up of an ideal
    • Finite maps of quasi-projective varieties
    • Dimension of quasi-projective algebraic sets
    • Zariski’s main theorem
    • Nonsingularity
    • Sheaves
    • Applications to regular and rational maps
    • Divisors
    • Differential forms and the canonical divisor
    • Schemes
    • The degree of a projective variety
    • Cohomology
    • Curves
    • An introduction to intersection theory
    • Surfaces
    • Ramification and étale maps
    • Bertini’s theorem and general fibers of maps
  • Reviews
     
     
    • The book is well written and self-contained; it contains both an introduction to the basics of the field and numerous advanced topics.

      Luca Ugaglia, Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1882018; 484 pp
MSC: Primary 14

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic \(0\) and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters.

With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Readership

Graduate students and researchers interested in algebraic geometry.

  • Chapters
  • A crash course in commutative algebra
  • Affine varieties
  • Projective varieties
  • Regular and rational maps of quasi-projective varieties
  • Products
  • The blow-up of an ideal
  • Finite maps of quasi-projective varieties
  • Dimension of quasi-projective algebraic sets
  • Zariski’s main theorem
  • Nonsingularity
  • Sheaves
  • Applications to regular and rational maps
  • Divisors
  • Differential forms and the canonical divisor
  • Schemes
  • The degree of a projective variety
  • Cohomology
  • Curves
  • An introduction to intersection theory
  • Surfaces
  • Ramification and étale maps
  • Bertini’s theorem and general fibers of maps
  • The book is well written and self-contained; it contains both an introduction to the basics of the field and numerous advanced topics.

    Luca Ugaglia, Mathematical Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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