Combinatorial Commutative Algebra

Paperback | June 21, 2005

byEzra Miller, Bernd Sturmfels

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

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From the Publisher

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

From the Jacket

Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eight...

Format:PaperbackDimensions:434 pages, 9.25 × 6.1 × 0 inPublished:June 21, 2005Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387237070

ISBN - 13:9780387237077

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Table of Contents

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

Editorial Reviews

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)