Concise introduction to algebraic varieties
Osserman, Brian
Concise introduction to algebraic varieties - Providence, Rhode Island : American Mathematical Society, 2021. - xvi, 259 pages : illustrations ; 26 cm. - Graduate studies in mathematics, v. 216 1065-7339 ; .
Includes bibliographical references (pages 247-249) and index.
Designed for a one-term 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 Riemann-Roch theorem, the Brill-Noether theorem, and applications.
The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set 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.
9781470466657
Algebraic varieties
Algebraic geometry--Instructional exposition (textbooks, tutorial papers, etc.)
Algebraic geometry--Foundations--Varieties and morphisms.
Algebraic geometry--Local theory--Singularities
512.7 / OSS-C
Concise introduction to algebraic varieties - Providence, Rhode Island : American Mathematical Society, 2021. - xvi, 259 pages : illustrations ; 26 cm. - Graduate studies in mathematics, v. 216 1065-7339 ; .
Includes bibliographical references (pages 247-249) and index.
Designed for a one-term 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 Riemann-Roch theorem, the Brill-Noether theorem, and applications.
The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set 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.
9781470466657
Algebraic varieties
Algebraic geometry--Instructional exposition (textbooks, tutorial papers, etc.)
Algebraic geometry--Foundations--Varieties and morphisms.
Algebraic geometry--Local theory--Singularities
512.7 / OSS-C
