A Generalization of the Taylor Complex Construction
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In this paper, given multigraded free resolutions of two monomial ideals, the authors construct a multi-generated free resolution of the sum of the two ideals, which is the same as the one in this paper.Abstract:
Given multigraded free resolutions of two monomial ideals, we construct a multigraded free resolution of the sum of the two idealsread more
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BookDOI
Edge Ideals: Algebraic and Combinatorial Properties
Susan Morey,Rafael H. Villarreal +1 more
TL;DR: A survey of algebraic and combinatorial properties of R/I(C) and C, respectively, can be found in this paper, where the authors give a criterion to estimate the regularity of the ideal of vertex covers of C. They also examine the associated primes of powers of edge ideals and show that these sets form an ascending chain.
Journal ArticleDOI
Matchings, coverings, and Castelnuovo-Mumford regularity
TL;DR: In this article, the co-chordal cover number of a graph G gives an upper bound for the Castelnuovo-Mumford regularity of the associated edge ideal.
Journal ArticleDOI
Matchings, coverings, and Castelnuovo-Mumford regularity
TL;DR: In this paper, the co-chordal cover number of a graph was shown to give an upper bound for the Castelnuovo-Mumford regularity of the associated edge ideal.
Book ChapterDOI
Regularity of Squarefree Monomial Ideals
TL;DR: A survey of the Castelnuovo-Mumford regularity of monomial ideals can be found in this paper, where the focus is on bounds and exact values for the regularity in terms of combinatorial data from associated simplicial complexes and/or hypergraphs.
Journal ArticleDOI
Results on the regularity of square-free monomial ideals
Huy Tài Hà,Russ Woodroofe +1 more
TL;DR: This note gives a recursive formula to compute the regularity of a vertex-decomposable hypergraph and shows that regularity in the graph case is bounded by a certain statistic based on maximal packings of nondegenerate star subgraphs.
References
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Book
Commutative Algebra: with a View Toward Algebraic Geometry
TL;DR: In this article, the authors define basic constructions and dimension theory, and apply them to the problem of homological methods for combinatorial problem solving in the context of homology.
Book
Cohen-Macaulay rings
Winfried Bruns,H. Jürgen Herzog +1 more
TL;DR: In this article, the authors present a self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules.
Posted Content
What can be computed in algebraic geometry
Dave Bayer,David Mumford +1 more
TL;DR: In this article, the main computational problems in algebraic geometry have been discussed, and a survey of the main results and bounds on their complexity has been given by the second author at a conference on Computer Algebra.
Journal ArticleDOI
Intersections of Leray complexes and regularity of monomial ideals
Gil Kalai,Roy Meshulam +1 more
TL;DR: If I, J are square-free monomial ideals in S = K[x1, ..., xn], then reg(I + J) ≤ reg( I) + reg(J) - 1, where reg (I) denotes the Castelnuovo-Mumford regularity of I.