Algebraic Geometry 1: From Algebraic Varieties to Schemes (Translations of Mathematical Monographs) (Vol 1) (Iwanami Series in Modern Mathematics) - Softcover

Kenji Ueno

Softcover

ISBN 10: 0821808621 ISBN 13: 9780821808627

Publisher: American Mathematical Society, 1999

Synopsis

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.

About this title

From the Publisher

This masterly written text, now also available to the international mathematical audience, tells its own tale and represents a highly welcome addition to the great standard textbooks on algebraic geometry.

Zentralblatt f\"ur Mathematik

Language Notes

Text: English (translation)
Original Language: Japanese

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• ISBN 10: 0821808621
• ISBN 13: 9780821808627
• Binding: Paperback
• Language: English
• Number of pages: 168