Softcover ISBN:  9781470471118 
Product Code:  GSM/222.S 
List Price:  $85.00 
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AMS Member Price:  $68.00 
eBook ISBN:  9781470471101 
EPUB ISBN:  9781470476588 
Product Code:  GSM/222.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471118 
eBook: ISBN:  9781470471101 
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 
Softcover ISBN:  9781470471118 
Product Code:  GSM/222.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470471101 
EPUB ISBN:  9781470476588 
Product Code:  GSM/222.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471118 
eBook ISBN:  9781470471101 
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 

Book DetailsGraduate Studies in MathematicsVolume: 222; 2022; 318 ppMSC: 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 RiemannRoch 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 BirkhoffGrothendieck 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 RiemannRoch Theorem.
ReadershipUndergraduate 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 RiemannRoch Theorem for curves

Background


Additional Material

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 graduatelevel introductory course in algebraic geometry. It covers the core topics from varieties to cohomology as a onesemester 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 wellchosen 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


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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 RiemannRoch 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 BirkhoffGrothendieck 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 RiemannRoch Theorem.
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 RiemannRoch 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 graduatelevel introductory course in algebraic geometry. It covers the core topics from varieties to cohomology as a onesemester 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 wellchosen 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