The depth of powers of an ideal

By Jürgen Herzog, Takayuki Hibi. 2004

172 citations recorded by the source corpus.

Abstract We study the limit and initial behavior of the numerical function f ( k ) = depth S / I k . General properties of this function together with concrete examples arising from combinatorics are discussed.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2876a7e10d074d75e90988f171ea51ad0c0d7585

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Persistence and stability properties of powers of ideals (2012, background): “This function has been first considered in [14] and subsequently for the edge ideals of a graph in [9].”
Edge ideals: algebraic and combinatorial properties (2010, background): “For a study of the initial and limit behaviour of the numerical function f(k) = depthR/Ik see [59].”
Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems (2006, background): “For a study of the initial and limit behavior of the numerical function f(k) = depthR/I see [21].”
Depths of Powers of the Edge Ideal of a Tree (2009, background): “A notable exception is the case where all powers of I have a linear resolution, which is discussed in [12].”
Powers of sums and their homological invariants (2016, background): “–Mumford regularity is regM= sup{i+j: Hi m(M)j6= 0} where Hi m(M) denotes the ith local cohomology of Mwith support in m. For more information on asymptotic properties of powers of ideals, see, e.g., [5, 9, 10, 11, 20, 21, 27, 39, 46] and their references. In this paper, we study several homological”