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 learn
i) 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.

David Mumford's first work in schemes was established in the literature as the Red Book long before it was formally published. It is still a standard, much-used reference on this subject. As a result it has been reprinted several times. This 2nd edition is augmented by another well-known, but now unavailable text of the author "Curves and their Jacobians" (62 pp) Includes supplementary material: sn.pub/extras

Autorentext

David Mumford was Professor of Applied Mathematics at Brown University. In 1974 he was awarded the Fields Medal at the International Congress of Mathematicians in Vancouver.

Klappentext

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 learn i) 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.

Inhalt
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.