Introduction to Algebraic Geometry
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-3518-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3518-9 (ISBN)
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.
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.
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.
Steven Dale Cutkosky, University of Missouri, Columbia, MO.
A crash course in commutative algebra
Affine varieties
Projective varieties
Regular and rational maps of quasi-projective varieties
Products
The blow-up of an ideal
Finite maps of quasi-projective varieties
Dimension of quasi-projective 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 etale maps
Bertini's theorem and general fibers of maps
Bibliography
Index.
| Erscheinungsdatum | 13.06.2018 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1020 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-3518-7 / 1470435187 |
| ISBN-13 | 978-1-4704-3518-9 / 9781470435189 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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