Introduction to commutative algebra and algebraic geometry. Transl. from the German by Michael Ackerman. With a preface by David Mumford
type: Item
instance of: scholarly article
title: Introduction to commutative algebra and algebraic geometry. Transl. from the German by Michael Ackerman. With a preface by David Mumford
zbMATH Open document ID: 1263.13001
DOI: 10.1007/978-1-4614-5987-3
author: E. Kunz
published in: Modern Birkhäuser Classics
publication date: 2013-01-02T00:00:00Z
review text: Ernst Kunz (born 1933) has published several outstanding textbooks in the course of his long academic career as both researcher and teacher in differential algebra, algebraic geometry, and commutative algebra at the University if Regensburg, Germany. Among his most popular books is certainly the unique text [Einführung in die kommutative Algebra und algebraische Geometrie. Vieweg Studium, Bd. 46, Aufbaukurs Mathematik. Braunschweig/Wiesbaden: Friedr. Vieweg \& Sohn. X, 239 S., 18 Fig., 185 Übungsaufg (1980; Zbl 0432.13001)]. Already this German original text came with an English preface by David Mumford for readers in the United States, mainly in order to have the novel flavor of this very special primer emphasized by one of the most renowned authorities in the field. In fact, the author's [loc. cit.] was the first textbook in the literature that developed the basic principles of both commutative algebra and the geometry of algebraic varieties in their close interrelation, thereby strictly following the didactic principle that certain areas of both subjects are best understood together, that is, in their natural combination. An English translation of the German edition of this book was provided in 1985 by Birkhäuser Verlag, with only a few major changes of the well-tried original text [the author, Introduction to commutative algebra and algebraic geometry. Transl. from the German by Michael Ackerman. With a preface by David Mumford. Boston-Basel-Stuttgart: Birkhäuser. X, 238 p. (1985; Zbl 0563.13001)]. The book under review is a reprint of just that English translation from 1985, without any further alterations or complements. Now as before, the main goal of the book is to lead the reader from the classical Kronecker problem of determining the minimal number of equations needed to define special (affine or projective) algebraic varieties to an exposition of Serre's famous problem on projective modules over polynomial rings. The development of the fundamental concept…
Mathematics Subject Classification ID: 13-02
Mathematics Subject Classification ID: 13-01
Mathematics Subject Classification ID: 14-01
Mathematics Subject Classification ID: 14Axx
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 13B30
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 01A75
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 14A10
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 13Cxx
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 97G99
zbMATH DE Number: 6121075
zbMATH Keywords: affine algebraic varieties
zbMATH Keywords: projective varieties
zbMATH Keywords: Kronecker problem
zbMATH Keywords: projective modules
zbMATH Keywords: Serre problem
zbMATH Keywords: local-global principle
reviewed by: Werner Kleinert
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4614-5987-3
OpenAlex ID: W1931868030
description: scientific article; zbMATH DE number 6121075