Hardcover ISBN:  9781470435189 
Product Code:  GSM/188 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470446703 
Product Code:  GSM/188.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470435189 
eBook: ISBN:  9781470446703 
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 
Hardcover ISBN:  9781470435189 
Product Code:  GSM/188 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470446703 
Product Code:  GSM/188.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470435189 
eBook ISBN:  9781470446703 
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 DetailsGraduate Studies in MathematicsVolume: 188; 2018; 484 ppMSC: 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.
ReadershipGraduate 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 quasiprojective varieties

Products

The blowup of an ideal

Finite maps of quasiprojective varieties

Dimension of quasiprojective 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


Additional Material

Reviews

The book is well written and selfcontained; it contains both an introduction to the basics of the field and numerous advanced topics.
Luca Ugaglia, Mathematical Reviews


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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.
Graduate students and researchers interested in algebraic geometry.

Chapters

A crash course in commutative algebra

Affine varieties

Projective varieties

Regular and rational maps of quasiprojective varieties

Products

The blowup of an ideal

Finite maps of quasiprojective varieties

Dimension of quasiprojective 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 selfcontained; it contains both an introduction to the basics of the field and numerous advanced topics.
Luca Ugaglia, Mathematical Reviews