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Translations of Mathematical Monographs: Algebraic Geometry 1 : From Algebraic Varieties to Schemes by American Mathem American Mathem (1999, Trade Paperback)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-100821808621
ISBN-139780821808627
eBay Product ID (ePID)244600
Product Key Features
Number of Pages154 Pages
LanguageEnglish
Publication NameAlgebraic Geometry 1 : from Algebraic Varieties to Schemes
Publication Year1999
SubjectGeometry / Algebraic
TypeTextbook
AuthorAmerican Mathem American Mathem
Subject AreaMathematics
SeriesTranslations of Mathematical Monographs
FormatTrade Paperback
Dimensions
Item Height0.4 in
Item Weight7.8 Oz
Item Length8.5 in
Item Width5.5 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN99-022304
Series Volume Number185
IllustratedYes
Volume NumberVol. 1
Table Of ContentAlgebraic varieties; Schemes; Categories and schemes; Solutions to problems; Solutions to exercises; Index; Copy/Reprinting page.
SynopsisBy studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties., This is the first of three volumes on algebraic geometry. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject. The book begins with a description of the standard theory of algebraic varieties. Next, sheaves are introduced and studied, using as few prerequisites as possible, and finally, Ueno describes schemes and their properties. Further properties of schemes will be discussed in the second volume. Ueno's book is a self-contained introduction to this important circle of ideas which assumes only a knowledge of basic notions from abstract algebra (such as prime ideals)., This is the first of three volumes on algebraic geometry. The second volume, ""Algebraic Geometry 2: Sheaves and Cohomology"", is available from the AMS as Volume 197 in the ""Translations of Mathematical Monographs"" series. Early in the 20th century, algebraic geometry underwent a significant overhaul, as mathematicians, notably Zariski, introduced a much stronger emphasis on algebra and rigor into the subject. This was followed by another fundamental change in the 1960s with Grothendieck's introduction of schemes. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them.Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject. The book begins with a description of the standard theory of algebraic varieties. Then, sheaves are introduced and studied, using as few prerequisites as possible. Once sheaf theory has been well understood, the next step is to see that an affine scheme can be defined in terms of a sheaf over the prime spectrum of a ring.By studying algebraic varieties over a field, Ueno demonstrates how the notion of schemes is necessary in algebraic geometry. This first volume gives a definition of schemes and describes some of their elementary properties. It is then possible, with only a little additional work, to discover their usefulness. Further properties of schemes will be discussed in the second volume. Ueno's book is a self-contained introduction to this important circle of ideas, assuming only a knowledge of basic notions from abstract algebra (such as prime ideals). It is suitable as a text for an introductory course on algebraic geometry., This is the first of three volumes on algebraic geometry. Most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an introduction to the theory, which should overcome any such impediment to learning this rich subject.
LC Classification NumberQA564.U3513 1999
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