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Algebraic Geometry : An Introduction - Catriona Maclean

Algebraic Geometry

An Introduction

By: Daniel Perrin, Catriona Maclean (Translator)

Paperback Published: 1st November 2007
ISBN: 9781848000551
Number Of Pages: 258

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Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

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From the reviews:

"The book under review, Algebraic Geometry, by Daniel Perrin, is an introductory text on modern algebraic geometry. It is aimed to be the text for a first basic course for graduate students. ... is very nicely written (and very nicely translated into English too). ... Perrin has included many, many remarks aimed to explain and deconstruct definitions and theorems. I believe these remarks will be very valuable to the reader in order to gain the very much needed intuition for the theory." (Alvaro Lozano-Robledo, MathDL, May, 2008)

"The book under review is the faithful translation into English of D. Perrin's popular French text 'Geometrie algebrique. Une introduction.' ... will be to the greatest benefit of the wide international community of students, teachers, and beginning researchers in the field of modern algebraic geometry. Also, we would like to emphasize again that this primer is perfectly suitable for a one-semester graduate course on the subject, and for profound self-study just as well." (Werner Kleinert, Zentralblatt MATH, Vol. 1132 (10), 2008)

"This is the English translation of an outstanding textbook, originally published in French. ... Appendices contain a summary of results from commutative algebra used in this book and a short introduction to scheme theory. Anyone looking for a textbook on algebraic geometry that starts with the basics and presents a lot of material in a digestible way ... will find this volume an excellent choice." (Ch. Baxa, Monatshefte fur Mathematik, Vol. 160 (4), July, 2010)

Introductionp. 1
Affine algebraic setsp. 9
Projective algebraic setsp. 25
Sheaves and varietiesp. 37
Dimensionp. 69
Tangent spaces and singular pointsp. 87
Bezout's theoremp. 101
Sheaf cohomologyp. 113
Arithmetic genus of curves and the weak Riemann-Roch theoremp. 131
Rational maps, geometric genus and rational curvesp. 149
Liaison of space curvesp. 173
Summary of useful results from algebrap. 199
Schemesp. 209
Problemsp. 215
Referencesp. 251
Index of notationsp. 253
Indexp. 255
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781848000551
ISBN-10: 1848000553
Series: Universitext
Audience: General
Format: Paperback
Language: English
Number Of Pages: 258
Published: 1st November 2007
Publisher: Springer London Ltd
Country of Publication: GB
Dimensions (cm): 23.52 x 16.23  x 1.4
Weight (kg): 0.4

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