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Kenji Ueno " Algebraic Geometry 1: From Algebraic Varieties to Schemes"

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.

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	Encyclopedias Algebraic Geometry I: Algebraic Curves Algebraic Manifolds and Schemes (Encyclopaedia of Mathematical Sciences) Algebraic Geometry I: Algebraic Curves Algebraic Manifolds and Schemes (Encyclopaedia of Mathematical Sciences)Springer \| 1994 \| ISBN: 0387519955 \| Pages: 307 \| DJVU \| 3.71 MBThis volume of the Encyclopaedia consists of two parts. The first ...
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	Mathematics Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians Parshin A.N., Shafarevich I.R (Ed.) ¡°Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians" Springer \| 1997-12-16 \| ISBN: 3540546812 \| Djvu \| 278 pages \| 2,4 Mb The first contribution of this EMS vo ...
	Mathematics Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians (Encyclopaedia of Mathematical Sciences) Author: Publisher: Springer (1997)Binding: Hardcover, 270 pagespricer: $139.00ISBN-10: 3540546812editorialreviewsThe first contribution of this EMS volume on complex algebraic geometry touches upon many of the central problems in this vast ...

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