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Hardcover ISBN:  9781470460136 
Product Code:  GSM/216 
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AMS Member Price:  $100.00 
Sale Price:  $81.25 
Softcover ISBN:  9781470466657 
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AMS Member Price:  $68.00 
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eBook ISBN:  9781470466640 
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Product Code:  GSM/216.E 
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AMS Member Price:  $68.00 
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Softcover ISBN:  9781470466657 
eBook ISBN:  9781470466640 
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AMS Member Price:  $136.00 $102.00 
Sale Price:  $110.50 $82.88 
Hardcover ISBN:  9781470460136 
eBook ISBN:  9781470466640 
Product Code:  GSM/216.B 
List Price:  $210.00 $167.50 
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Book DetailsGraduate Studies in MathematicsVolume: 216; 2021; 259 ppMSC: Primary 14
Designed for a oneterm introductory course on algebraic varieties over an algebraically closed field, this book prepares students to continue either with a course on schemes and cohomology, or to learn more specialized topics such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the RiemannRoch theorem, the BrillNoether theorem, and applications.
The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic pointset topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
ReadershipUndergraduate and graduate students interested in an introduction to fundamentals of algebraic geometry.

Table of Contents

Chapters

Introduction: An overview of algebraic geometry through the lens of plane curves

Affine algebraic varieties

Regular functions and morphisms

Singularities

Abstract varieties via atlases

Projective varieties

Nonsingular curves and complete varieties

Divisors on nonsingular curves

Differential forms

An invitation to the theory of algebraic curves

Complex varieties and the analytic topology

A roadmap through algebra


Additional Material

Reviews

For a quick and readerfriendly short introduction to algebraic varieties, this new book could be a nice choice for a onesemester course. With a minimum of commutative algebra background, summarized in one appendix, and a bare minimum of pointset topology, this textbook covers the basics of abstract algebraic varieties over an algebraically closed field. From affine varieties and regular functions and morphisms on them, vanishing ideals, rational maps, dimension, tangent spaces and singularities, to abstract algebraic varieties, including the important example of projective varieties with its homogeneous ideals and coordinate rings, the book systematically develops the theory with plenty of examples and many exercises interspersed throughout the text.
...Comparing this textbook with others on the same level, the result is favorable: The approach is fresh, accessible with a basic background on commutative algebra, and with a good mixture of local and global aspects with motivations, examples and wellchosen proofs that balance the algebraic and geometric sides of a given topic.
Felipe Zaldivar, Universidad Autonoma MetropolitanaI


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Designed for a oneterm introductory course on algebraic varieties over an algebraically closed field, this book prepares students to continue either with a course on schemes and cohomology, or to learn more specialized topics such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the RiemannRoch theorem, the BrillNoether theorem, and applications.
The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic pointset topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
Undergraduate and graduate students interested in an introduction to fundamentals of algebraic geometry.

Chapters

Introduction: An overview of algebraic geometry through the lens of plane curves

Affine algebraic varieties

Regular functions and morphisms

Singularities

Abstract varieties via atlases

Projective varieties

Nonsingular curves and complete varieties

Divisors on nonsingular curves

Differential forms

An invitation to the theory of algebraic curves

Complex varieties and the analytic topology

A roadmap through algebra

For a quick and readerfriendly short introduction to algebraic varieties, this new book could be a nice choice for a onesemester course. With a minimum of commutative algebra background, summarized in one appendix, and a bare minimum of pointset topology, this textbook covers the basics of abstract algebraic varieties over an algebraically closed field. From affine varieties and regular functions and morphisms on them, vanishing ideals, rational maps, dimension, tangent spaces and singularities, to abstract algebraic varieties, including the important example of projective varieties with its homogeneous ideals and coordinate rings, the book systematically develops the theory with plenty of examples and many exercises interspersed throughout the text.
...Comparing this textbook with others on the same level, the result is favorable: The approach is fresh, accessible with a basic background on commutative algebra, and with a good mixture of local and global aspects with motivations, examples and wellchosen proofs that balance the algebraic and geometric sides of a given topic.
Felipe Zaldivar, Universidad Autonoma MetropolitanaI