Combinatorial Commutative Algebra

• Main Authors: Miller, Ezra (Author), Sturmfels, Bernd (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Series: Graduate Texts in Mathematics, 227
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Combinatorics.; Commutative Rings and Algebras.; Algebraic Geometry.

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 algebra...

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.