The Red Book of Varieties and Schemes

Produktbeschreibung

Mumford's famous Red Book gives a simple readable account of the basic
objects of algebraic geometry, preserving as much as possible their geometric
flavor and integrating this with the tools of commutative algebra. It is
aimed at graduate students or mathematicians in other fields wishing to
learn quickly what algebraic geometry is all about. This new edition also
includes an overview of the theory of curves, their moduli spaces and their
Jacobians, one of the most exciting fields within algebraic geometry. The
book is aimed at graduate students and professors seeking to learni) the
concept of "scheme" as part of their study of algebraic geometry and ii)
an overview of moduli problems for curves and of the use of theta functions
to study these. 

Inhaltsverzeichnis

Varieties.- Preschemes.- Local properties of schemes.- References.- Appendix: Curves and their Jacobians.- Survey of work on the Schottky problem up to 1996 (by Enrico Arbarello).- References.- Guide to the Literature and References (Curves and Their Jacobians).- Supplementary Bibliography on the Schottky Problem. 

Kritik

"This is the second edition of a famous and well-known introduction to algebraic geometry, written to show that the language of schemes is fundamentally geometrical and clearly expressing the intuition of algebraic geometry. ... This book can strongly be recommended to anybody interested in algebraic geometry and willing to learn about varieties and schemes and their main problems."
EMS Newsletter, Vol. 37, Sept. 2000 

Autoreninfo

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.
Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.