Packed with contributions from international experts, Commutative Algebra: Geometric, Homological, Combinatorial, and Computational Aspects features new research results that borrow methods from neighboring fields such as combinatorics, homological algebra, polyhedral geometry, symbolic computation, and topology. This book consists of articles presented during two conferences held in Spain and Portugal in June, 2003. It encompasses a variety of topics, including blowup algebras, Castelnuovo-Mumford regularity, integral closure and normality, Koszul homology, liaison theory, multiplicities, polarization, and reductions of ideals. This comprehensive volume will stimulate further research in the field.
Table of Contents
A Theorem of Eakin and Sathaye and Green's Hyperplane Restriction Theorem. Liaison of Varieties of Small Dimension and Deficiency Modules. Regularity Jumps for Powers of Ideals. Integral Closure of Ideals and Annihilators of Homology. Poincaré Series of Surface Singularities. Multi-Graded Hilbert Coefficients. Torsion Freeness and Normality of Blowup Rings of Monomial Ideals. Monomial Ideals via Square-Free Monomial Ideals. When Does the Equality I2=QI Hold True in Buchsbaum Rings? Integral Closures of Ideals in Completions of Regular Local Domains. The Components of a Variety of Matrices with Square Zero and Submaximal Rank. The Support of Top Graded Local Cohomology Modules. An Approach to the Uniform Artin-Rees Theorems from the Notion of Relation Type. Castelnuovo-Mumford Regularity and Finiteness of Hilbert Functions. Differential Idealizers and Algebraic Free Divisors. Gorenstein Rings Call the Tune. On Free Integral Extensions Generated by One Element. Degeneration of G-Dimension of Modules.