文档介绍：mutative Algebra
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Ezra Miller and Bernd Sturmfels
18 October 2004
To Elen and Hyungsook
Preface
The last decade has seen a number of exciting developments at the inter-
section mutative algebra binatorics. New methods have
evolved out of an influx of ideas from such diverse areas as polyhedral
geometry, theoretical physics, representation theory, homological algebra,
symplectic geometry, graph theory, integer programming, -
putation, and statistics. The purpose of this volume is to provide a self-
contained introduction to some of the binatorial techniques for
dealing with polynomial rings, semigroup rings, and determinantal rings.
Our exposition mainly binatorially defined ideals and their
quotients, with a focus on numerical invariants and resolutions, especially
under gradings more refined than the standard integer grading.
This project started at the COCOA summer school in Torino, Italy, in
June 1999. The eight lectures on monomial ideals given there by Bernd
Sturmfels were later written up by Ezra Miller and David Perkinson and
published in [MP01]. We felt it would be nice to add more material and
turn the COCOA notes into a real book. What you hold in your hand is
the result, with Part I being a direct outgrowth of the COCOA notes.
mutative algebra is a broad area of mathematics, and
one can cover but a small selection of the possible topics in a single book.
Our choices were motivated by our research interests and by our desire
to reach a wide audience of students and researchers in neighboring fields.
Numerous references, mostly confined to the Notes ending each chapter,
point the reader to closely related topics that we were unable to cover.
A milestone in the development mutative algebra
was the 1983 book by Richard Stanley [Sta96]. That book, now in its
second edition, is still an excellent source. We have made an attempt to
complement and build on the material covered by Stanley. Another boon