Algebraic geometry II
type: Item
instance of: scholarly article
title: Algebraic geometry II
zbMATH Open document ID: 1325.14001
author: Tadao Oda
author: David Mumford
published in: Texts and Readings in Mathematics
publication date: 2015-10-06T00:00:00Z
review text: This volume is a sequel to \textit{David Mumford}'s classical textbook [Algebraic Geometry. I: Complex projective varieties. Berlin: Springer-Verlag (1976; Zbl 0356.14002); see also Reprint of the corr. 2nd print. (1995; Zbl 0821.14001)], which first appeared almost 40 years ago. In fact, the genesis of this considerably delayed second volume is rather amazing, and can be briefly summarized as follows. It is well-known that Fields medalist David Mumford (born 1937) worked in algebraic geometry and related fields from 1959 until 1982, before his research interests shifted to areas in applied mathematics such as pattern theory, shape theory, vision theory, neuronal architectures, and stochastic models. During the first period of his academic career, D. Mumford gave various introductory courses in algebraic geometry at Harvard University, and he once aimed to publish the continuously evolving course notes as a three-volume textbook. However, what was really published is a preliminary version of the first three chapters, which appeared in 1967 as mimeographed notes bound with a red cover, the famous ``Red book'', and the above-mentioned first volume ``Algebraic geometry I'' [Zbl 0821.14001] of the originally planned textbook series. The mimeographed ``Red book'' from 1967 is now available as Springer Lecture Notes under the title ``The red book of varieties and schemes'' [Zbl 0658.14001; Zbl 0945.14001], and as such it still is one of the great, most popular classics among the textbooks in modern algebraic geometry. The intended volume ``Algebraic geometry II'' of the planned book series would have been based on the material of the ``Red book'', on the one hand, and on existing but unpublished notes of D. Mumford on the other. However, due to the appearance of \textit{R. Hartshorne}'s famous textbook [Algebraic geometry. York-Heidelberg-Berlin: Springer-Verlag (1977; Zbl 0367.14001)] in the meantime, which already covered a good part of the material he had planned to in…
reviewed by: Werner Kleinert
Mathematics Subject Classification ID: 14-01
Mathematics Subject Classification ID: 14A15
Mathematics Subject Classification ID: 14F06
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14F25
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 6489981
zbMATH Keywords: textbook (algebraic geometry)
zbMATH Keywords: schemes
zbMATH Keywords: morphisms
zbMATH Keywords: sheaves
zbMATH Keywords: lije bundles
zbMATH Keywords: ampleness
zbMATH Keywords: cohomology
zbMATH Keywords: group schemes
zbMATH Keywords: differentials
zbMATH Keywords: multiplicities
zbMATH Keywords: deformation theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6489981