Algebraic Geometry: A First Course by Joe Harris (English) Hardcover Book

Description: Algebraic Geometry by Joe Harris 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description This book is intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. It thus emplasizes the classical roots of the subject. For readers interested in simply seeing what the subject is about, this avoids the more technical details better treated with the most recent methods. For readers interested in pursuing the subject further, this book will provide a basis for understanding the developments of the last half century, which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard Universities, this book retains the informal style of the lectures and stresses examples throughout; the theory is developed as needed. The first part is concerned with introducing basic varieties and constructions; it describes, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic groups. The second part discusses attributes of varieties, including dimension, smoothness, tangent spaces and cones, degree, and parameter and moduli spaces. Notes 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. Author Biography "Benedict Gross" is the Leverett Professor of Mathematics and Dean of Harvard College. "Joe Harris" is the Higgins Professor of Mathematics and Chair of the Mathematics Department at Harvard. Table of Contents 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. Review J. HarrisAlgebraic GeometryA First Course"This book succeeds brilliantly by concentrating on a number of core topics (the rational normal curve, Veronese and Segre maps, quadrics, projections, Grassmannians, scrolls, Fano varieties, etc.) and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship."—MATHEMATICAL REVIEWS Promotional Corrected 3rd printing Long Description 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. Review Text J. Harris Algebraic Geometry A First Course "This book succeeds brilliantly by concentrating on a number of core topics (the rational normal curve, Veronese and Segre maps, quadrics, projections, Grassmannians, scrolls, Fano varieties, etc.) and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship."a? MATHEMATICAL REVIEWS Review Quote J. HarrisAlgebraic GeometryA First Course"This book succeeds brilliantly by concentrating on a number of core topics (the rational normal curve, Veronese and Segre maps, quadrics, projections, Grassmannians, scrolls, Fano varieties, etc.) and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship."-MATHEMATICAL REVIEWS Description for Sales People 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. Details ISBN0387977163 Author Joe Harris Short Title ALGEBRAIC GEOMETRY Series Graduate Texts in Mathematics Language English ISBN-10 0387977163 ISBN-13 9780387977164 Media Book Format Hardcover DEWEY 516.35 Series Number 133 Imprint Springer-Verlag New York Inc. Subtitle A First Course Place of Publication New York, NY Country of Publication United States Residence US Edition 1st DOI 10.1007/b43351;10.1007/978-1-4757-2189-8 AU Release Date 1995-12-01 NZ Release Date 1995-12-01 UK Release Date 1995-12-01 Pages 330 Publisher Springer-Verlag New York Inc. Edition Description 1st ed. 1992. Corr. 3rd printing 1995 Alternative 9781441930996 Illustrations XIX, 330 p. Audience Postgraduate, Research & Scholarly Year 1992 Publication Date 1992-09-17 US Release Date 1992-09-17 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! 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