Overview

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Full Product Details

Author:   Ezra Miller ,  Bernd Sturmfels
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2005 ed.
Volume:   227
Dimensions:   Width: 15.60cm , Height: 2.30cm , Length: 23.40cm
Weight:   1.750kg
ISBN:  

9780387223568

ISBN 10:   0387223568
Pages:   420
Publication Date:   21 December 2004
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plücker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.

Reviews

From the reviews: <p> The book is a selfcontained introduction to some of the combinatorial techniques for dealing with multigraded polynomial rings, semigroup rings, and determinantal rings. a ] Each chapter begins with an overview and ends with notes and references. a ] It is interesting for a wide audience of students and researchers. a ] The book may serve as a basis for a full year course on this topic. It contains a lot of exercises and hints for further studies. (Gerhard Pfister, Zentralblatt MATH, Vol. 1066, 2005) <p> That the current text will have a significant influence on the new generation of combinatorially inclined commutative algebraists is a ] doubtless. a ] There are a great number of important and motivating examples throughout the text. Further examples, challenges and open problems are given in the exercises at the end of each chapter. The notes after the chapters are very helpful for giving the right chronological perspective and suggesting further reading. The text can serve as a basis for several graduate courses. (Joseph Gubeladze, Mathematical Reviews, Issue 2006 d) <p> The aim of this book is to present techniques for the study of certain combinatorially defined ideals in graded rings R, such as polynomial rings. This concerns mostly the construction of resolutions of these ideals and the computation of corresponding invariants (e.g. the Hilbert-series, syzygies, Betti-numbers). a ] the authors explain most of the necessary background in order to understand their diverse applications, most of which concern problems in Algebraic Geometry a ] . (J. Mahnkopf, Monatshefte fA1/4r Mathematik, Vol. 147 (4), 2006) <p> Recently, there has been muchinteraction between combinatorics and commutative algebra, and the authorsa (TM) aim has been an introduction to this area which is self-contained a ] . A clear account which touches on many classical concepts not usually mentioned. (Mathematika, Vol. 52, 2005)

From the reviews: The book under review constitutes a self-contained introduction to the use of combinatorial methods in commutative algebra. ... Concrete calculations and examples are used to introduce and develop concepts. Numerous exercises provide the opportunity to work through the material and end of chapter notes comment on the history and development of the subject. The authors have provided us with a useful reference and an effective text book. (R. J. Shank, Zentralblatt MATH, Vol. 1090 (16), 2006)

"From the reviews: ""The book under review constitutes a self-contained introduction to the use of combinatorial methods in commutative algebra. … Concrete calculations and examples are used to introduce and develop concepts. Numerous exercises provide the opportunity to work through the material and end of chapter notes comment on the history and development of the subject. The authors have provided us with a useful reference and an effective text book."" (R. J. Shank, Zentralblatt MATH, Vol. 1090 (16), 2006)"

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