Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman

Publication date: 8 December 1996

Published in: Algorithms and Computation in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Gröbner bases ring of invariants syzygies Hilbert function radical Jacobian ideal primary decomposition integral closure Nullstellensätze Macaulay computational aspects ideal transform degree of complexity algorithms in algebra computation of cohomology JFM 52.0127.01

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry (14-01) Transcendental field extensions (12F20) Relevant commutative algebra (14A05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra (13-01) Computational aspects in algebraic geometry (14Qxx) Computational aspects and applications of commutative rings (13Pxx)

Related Items

On the number of generators of the torsion module of differentials, Higher relative primitive ideals, Unnamed Item, Asymptotic behavior of reduction numbers, A Constructive Approach to the Module of Twisted Global Sections on Relative Projective Spaces, Elementary construction of residue currents associated to Cohen–Macaulay ideals, ANALYTIC SPREAD AND INTEGRAL CLOSURE OF INTEGRALLY DECOMPOSABLE MODULES, On the complexity of the integral closure, CRITICAL BINOMIAL IDEALS OF NORTHCOTT TYPE, Quantitative sheaf theory, A commutative algebra approach to multiplicative Hom-Lie algebras, Elementary construction of the minimal free resolution of the Specht ideal of shape \((n -d,d)\), On Hilbert coefficients and sequentially generalized Cohen–Macaulay modules, Comparing invariants of toric ideals of bipartite graphs, A signature-based algorithm for computing the nondegenerate locus of a polynomial system, The isomorphism problem of projective schemes and related algorithmic problems, Normality of Rees algebras of generalized mixed product ideals, On regularity of Rees algebras of edge ideals of cone graphs, Canonical modules and class groups of Rees-like algebras, Regularity and ℎ-polynomials of toric ideals of graphs, A commutative algebraic approach to the fitting problem, Computation of a specified root of a polynomial system of equations using eigenvectors, First coefficient ideals and the \(S_2\)-ification of a Rees algebra, Computing the radical of an ideal in positive characteristic, Computing bases of complete intersection rings in Noether position, Footprint and minimum distance functions, On computing the integral closure, Irreducibility of ideals in a one-dimensional analytically irreducible ring, Detecting flat normal cones using Segre classes., Castelnuovo-Mumford regularity of Ext modules and homological degree, Extended degree functions and monomial modules, On the Integral Degree of Integral Ring Extensions, Castelnuovo–Mumford regularity of associated graded modules of k-Buchsbaum modules, On the Irreducible Components of the Form Ring and an Application to Intersection Cycles, Rings of Constants of the Formk[f], Homological invariants of Cameron–Walker Graphs, Generalized Integral Dependence Relations, Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs, Castelnuovo–Mumford Regularity of Associated Graded Modules and Fiber Cones of Filtered Modules, Computing representation matrices for the action of Frobenius on cohomology groups, Standard pairs for monomial ideals in semigroup rings, Computing in algebraic geometry and commutative algebra using Macaulay 2, Regularity and \(h\)-polynomials of binomial edge ideals, Analysis of an algorithm to compute the cohomology groups of coherent sheaves and its applications, Computing global dimension of endomorphism rings via ladders, Noether normalization guided by monomial cone decompositions, The primary components of positive critical binomial ideals, Multigraded modules of nested type, Canonical state representations and Hilbert functions of multidimensional systems, Irreducible decomposition of binomial ideals, Castelnuovo-Mumford regularity of canonical and deficiency modules, Castelnuovo-Mumford regularity of initial ideals, The computation of purity filtrations over commutative Noetherian rings of operators and their application to behaviors, Algebraic properties of the coordinate ring of a convex polyomino, The determination of integral closures and geometric applications, The integral closure of subrings associated to graphs, Asymptotic behaviour of monomial ideals on regular sequences, Castelnuovo-Mumford regularity and computing the de Rham cohomology of smooth projective varieties, Generalization of the Lee-O'Sullivan list decoding for one-point AG codes, Symbolic powers of perfect ideals of codimension 2 and birational maps, Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields, Indices of normalization of ideals, Algebraic observations on the Jacobian conjecture., An algorithm for computing invariants of linear actions of algebraic groups up to a given degree., Castelnuovo–Mumford Regularity of Some Modules, Continuity properties for flat families of polynomials. I: Continuous parametrizations, Hilbert coefficients and sequentially Cohen-Macaulay modules, On implicit systems of differential equations., Effective computation of symbolic powers by jacobian matrices, Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals, Symbolic powers of edge ideals., Effective normality criteria for algebras of linear type., Cohomology of projective schemes: From annihilators to vanishing., Singularities of Rees-like algebras, The construction of Noetherian operators, Rees algebra over an ideal in \(\mathfrak{t}\)-rings, Alexander duality for Stanley-Reisner rings and squarefree \(\mathbb{N}^n\)-graded modules, Algorithms for graded injective resolutions and local cohomology over semigroup rings, Computation of unirational fields, Differential operators on orbifolds, Essential components of an algebraic differential equation, The Schmidt-Kolchin conjecture, Regularity and algebraic properties of certain lattice ideals, Bounds in cohomology, The relation type of affine algebras and algebraic varieties, On the structure of the fiber cone of ideals with analytic spread one, An effective avoidance principle for a class of ideals, List decoding algorithm based on voting in Gröbner bases for general one-point AG codes, A generalization of Gröbner bases helps to compute singularity theory transformations, ON THE NORMALITY OF MONOMIAL IDEALS OF MIXED PRODUCTS, Computing invariants of algebraic groups in arbitrary characteristic, Irreducible affine space curves and the uniform Artin-Rees property on the prime spectrum, Lexsegment ideals and their \(h\)-polynomials, Depth and regularity of monomial ideals via polarization and combinatorial optimization, The equations of almost complete intersections, Relations between roots and coefficients, interpolation and application to system solving, The slopes determined by \(n\) points in the plane, Homology of homogeneous divisors, Primary decomposition of zero-dimensional ideals over finite fields, Complexity bounds on Semaev's naive index calculus method for ECDLP, Prony's method under an almost sharp multivariate Ingham inequality, Polynomial extensions of IDF-domains and of IDPF-domains, An extension of a theorem of Frobenius and Stickelberger to modules of projective dimension one over a factorial domain, Regularity bound of generalized binomial edge ideal of graphs, Regularity and \(a\)-invariant of Cameron-Walker graphs, Using symmetries in the eigenvalue method for polynomial systems, Low-dimensional singularities with free divisors as discriminants, Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence, Matching numbers and dimension of edge ideals, On adjusted Hilbert-Samuel functions, Bipartite graphs whose edge algebras are complete intersections, On the complexity of counting components of algebraic varieties, Cohomology and toric varieties and local cohomology with monomial supports, Factorization-free decomposition algorithms in differential algebra, Local cohomology at monomial ideals, Computing global extension modules, Inequalities of invariants on Stanley-Reisner rings of Cohen-Macaulay simplicial complexes, Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals, Sally’s question and a conjecture of shimoda, Projective dimension in UFDs, Conormal modules via primitive ideals, Around the Eakin-Sathaye theorem, A note on the Rees algebra of a bipartite graph, Computer algebra and algebraic geometry -- achievements and perspectives, Flatness and fibred powers over smooth varieties, Normality of semigroups with some links to graph theory., A Local Flatness Criterion for Complete Modules, On flattening of coherent sheaves and of projective morphisms, Symmetry, invariants, and topology in molecular models, Normality criteria for monomial ideals, Index of nilpotency of binomial ideals., The inverse Gröbner basis problem in codimension two., Generalizations of a lemma of Freudenburg, A duality theorem for the ic-resurgence of edge ideals, Algorithmic computation of flattenings and of modular deformations, Computing characteristic classes of projective schemes., A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors, Unimodular triangulations and coverings of configurations arising from root systems

Uses Software