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Cover: 9780387977164 | Algebraic Geometry | A First Course | Joe Harris | Buch | XIX | 1995
Bild: 9780387977164 | Algebraic Geometry | A First Course | Joe Harris | Buch | XIX | 1995
Cover: 9780387977164 | Algebraic Geometry | A First Course | Joe Harris | Buch | XIX | 1995
Bild: 9780387977164 | Algebraic Geometry | A First Course | Joe Harris | Buch | XIX | 1995
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Algebraic Geometry
A First Course
Buch von Joe Harris
Sprache: Englisch

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Beschreibung
This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners.
This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners.
Zusammenfassung
This book provides an elementary introduction to algebraic geometry. The reader is introduced to principal objects, methods and goals of the subject. Theory is developed concurrently with many examples and exercises enabling the student to better understand the subject matter. Prerequisites include some linear and multilinear algebra and a basic background in abstract algebra.
Inhaltsverzeichnis
I: Examples of Varieties and Maps.- Lecture 1 Affine and Projective Varieties.- Lecture 2 Regular Functions and Maps.- Lecture 3 Cones, Projections, and More About Products.- Lecture 4 Families and Parameter Spaces.- Lecture 5 Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz.- Lecture 6 Grassmannians and Related Varieties.- Lecture 7 Rational Functions and Rational Maps.- Lecture 8 More Examples.- Lecture 9 Determinantal Varieties.- Lecture 10 Algebraic Groups.- II: Attributes of Varieties.- Lecture 11 Definitions of Dimension and Elementary Examples.- Lecture 12 More Dimension Computations.- Lecture 13 Hilbert Polynomials.- Lecture 14 Smoothness and Tangent Spaces.- Lecture 15 Gauss Maps, Tangential and Dual Varieties.- Lecture 16 Tangent Spaces to Grassmannians.- Lecture 17 Further Topics Involving Smoothness and Tangent Spaces.- Lecture 18 Degree.- Lecture 19 Further Examples and Applications of Degree.- Lecture 20 Singular Points and Tangent Cones.- Lecture 21 Parameter Spaces and Moduli Spaces.- Lecture 22 Quadrics.- Hints for Selected Exercises.- References.
Details
Erscheinungsjahr: 1992
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 356
Reihe: Graduate Texts in Mathematics
Inhalt: xix
330 S.
ISBN-13: 9780387977164
ISBN-10: 0387977163
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Harris, Joe
Auflage: 1992
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 25 mm
Von/Mit: Joe Harris
Erscheinungsdatum: 17.09.1992
Gewicht: 0,699 kg
preigu-id: 104859058
Zusammenfassung
This book provides an elementary introduction to algebraic geometry. The reader is introduced to principal objects, methods and goals of the subject. Theory is developed concurrently with many examples and exercises enabling the student to better understand the subject matter. Prerequisites include some linear and multilinear algebra and a basic background in abstract algebra.
Inhaltsverzeichnis
I: Examples of Varieties and Maps.- Lecture 1 Affine and Projective Varieties.- Lecture 2 Regular Functions and Maps.- Lecture 3 Cones, Projections, and More About Products.- Lecture 4 Families and Parameter Spaces.- Lecture 5 Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz.- Lecture 6 Grassmannians and Related Varieties.- Lecture 7 Rational Functions and Rational Maps.- Lecture 8 More Examples.- Lecture 9 Determinantal Varieties.- Lecture 10 Algebraic Groups.- II: Attributes of Varieties.- Lecture 11 Definitions of Dimension and Elementary Examples.- Lecture 12 More Dimension Computations.- Lecture 13 Hilbert Polynomials.- Lecture 14 Smoothness and Tangent Spaces.- Lecture 15 Gauss Maps, Tangential and Dual Varieties.- Lecture 16 Tangent Spaces to Grassmannians.- Lecture 17 Further Topics Involving Smoothness and Tangent Spaces.- Lecture 18 Degree.- Lecture 19 Further Examples and Applications of Degree.- Lecture 20 Singular Points and Tangent Cones.- Lecture 21 Parameter Spaces and Moduli Spaces.- Lecture 22 Quadrics.- Hints for Selected Exercises.- References.
Details
Erscheinungsjahr: 1992
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 356
Reihe: Graduate Texts in Mathematics
Inhalt: xix
330 S.
ISBN-13: 9780387977164
ISBN-10: 0387977163
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Harris, Joe
Auflage: 1992
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 25 mm
Von/Mit: Joe Harris
Erscheinungsdatum: 17.09.1992
Gewicht: 0,699 kg
preigu-id: 104859058
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