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Algebraic Geometry: Notes on a Course
 
Michael Artin Massachusetts Institute of Technology, Cambridge, MA
Algebraic Geometry
Softcover ISBN:  978-1-4704-7111-8
Product Code:  GSM/222.S
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-7110-1
EPUB ISBN:  978-1-4704-7658-8
Product Code:  GSM/222.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7111-8
eBook: ISBN:  978-1-4704-7110-1
Product Code:  GSM/222.S.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
Algebraic Geometry
Click above image for expanded view
Algebraic Geometry: Notes on a Course
Michael Artin Massachusetts Institute of Technology, Cambridge, MA
Softcover ISBN:  978-1-4704-7111-8
Product Code:  GSM/222.S
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-7110-1
EPUB ISBN:  978-1-4704-7658-8
Product Code:  GSM/222.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7111-8
eBook ISBN:  978-1-4704-7110-1
Product Code:  GSM/222.S.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2222022; 318 pp
    MSC: Primary 14

    This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course.

    The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. \(\mathcal{O}\)-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line.

    Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in \(\mathbb{P}^3\), and double planes, and it ends with applications of the Riemann-Roch Theorem.

    Readership

    Undergraduate and graduate students interested in learning and teaching algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • Plane curves
    • Affine algebraic geometry
    • Projective algebraic geometry
    • Integral morphisms
    • Structure of varieties in the Zariski topology
    • Modules
    • Cohomology
    • The Riemann-Roch Theorem for curves
    • Background
  • Reviews
     
     
    • The expository book under review is an expansion of the lecture notes grown out of a course in algebraic geometry that the author taught at MIT seven times within the last twelve years. That is why the book, which the author likes to refer to as lecture notes, benefits from a fresh living expository style. The output is not that of a plastered grey collection of notions but rather the logbook of an original educational journey in which the author flies like an eagle at high altitude without missing any detail on the ground thanks to its long view, driving his young companions past the marvels of the mathematical landscapes. Or it may look like an ancient workshop, similar to those of the great Italian painters and sculptors, where the master enabled disciples to learn the art by imitation and absorption.

      Letterio Gatto (Polytechnic University of Turin), MathSciNet Mathematical Reviews Clippings
    • Overall, Artin's text offers an excellent graduate-level introductory course in algebraic geometry. It covers the core topics from varieties to cohomology as a one-semester course that can be taken without a prior class in commutative algebra. Artin shares valuable insights of what is essential to algebraic geometry and where one should focus to appreciate the bigger picture and cautions the reader of technical pitfalls and points of confusion. He provides motivation and well-chosen examples that train the readers' intuition. Moreover, the style is personal and inviting, like a professor talking with students. The book offers the chance to be his student, an experience I enjoyed and learned from by reading 'Algebraic: Notes on a Course.'

      David Murphy (Hillsdale College), MAA Reviews
    • The present book under review entitled "Algebraic Geometry - Notes on a Course," by Michael Artin is, according to my very subjective viewpoint, one of the best textbooks devoted to basics on algebraic geometry. I am aware of the fact that this is a rather bold statement, but I will try to justify my claim here. There are many textbooks devoted to the foundations of algebraic geometry, and it seems that there is no room for new ideas or strategies in writing such books. Everything has been tried. This was also my first prediction before receiving this book, and I can honestly say that I am very happy to have been wrong.

      Piotr Pokora (Kraków), zbMathOpen
  • 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: 2222022; 318 pp
MSC: Primary 14

This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course.

The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. \(\mathcal{O}\)-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line.

Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in \(\mathbb{P}^3\), and double planes, and it ends with applications of the Riemann-Roch Theorem.

Readership

Undergraduate and graduate students interested in learning and teaching algebraic geometry.

  • Chapters
  • Plane curves
  • Affine algebraic geometry
  • Projective algebraic geometry
  • Integral morphisms
  • Structure of varieties in the Zariski topology
  • Modules
  • Cohomology
  • The Riemann-Roch Theorem for curves
  • Background
  • The expository book under review is an expansion of the lecture notes grown out of a course in algebraic geometry that the author taught at MIT seven times within the last twelve years. That is why the book, which the author likes to refer to as lecture notes, benefits from a fresh living expository style. The output is not that of a plastered grey collection of notions but rather the logbook of an original educational journey in which the author flies like an eagle at high altitude without missing any detail on the ground thanks to its long view, driving his young companions past the marvels of the mathematical landscapes. Or it may look like an ancient workshop, similar to those of the great Italian painters and sculptors, where the master enabled disciples to learn the art by imitation and absorption.

    Letterio Gatto (Polytechnic University of Turin), MathSciNet Mathematical Reviews Clippings
  • Overall, Artin's text offers an excellent graduate-level introductory course in algebraic geometry. It covers the core topics from varieties to cohomology as a one-semester course that can be taken without a prior class in commutative algebra. Artin shares valuable insights of what is essential to algebraic geometry and where one should focus to appreciate the bigger picture and cautions the reader of technical pitfalls and points of confusion. He provides motivation and well-chosen examples that train the readers' intuition. Moreover, the style is personal and inviting, like a professor talking with students. The book offers the chance to be his student, an experience I enjoyed and learned from by reading 'Algebraic: Notes on a Course.'

    David Murphy (Hillsdale College), MAA Reviews
  • The present book under review entitled "Algebraic Geometry - Notes on a Course," by Michael Artin is, according to my very subjective viewpoint, one of the best textbooks devoted to basics on algebraic geometry. I am aware of the fact that this is a rather bold statement, but I will try to justify my claim here. There are many textbooks devoted to the foundations of algebraic geometry, and it seems that there is no room for new ideas or strategies in writing such books. Everything has been tried. This was also my first prediction before receiving this book, and I can honestly say that I am very happy to have been wrong.

    Piotr Pokora (Kraków), zbMathOpen
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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