Saturation and Castelnuovo–Mumford regularity

By I. Bermejo, Philippe Gimenez. 2006

74 citations recorded by the source corpus.

Abstract Let I be a homogeneous ideal of the polynomial ring K [ x 0 , … , x n ] , where K is an arbitrary field. Avoiding the construction of a minimal graded free resolution of I , we provide effective methods for computing the Castelnuovo–Mumford regularity of I that also compute other cohomological invariants of K [ x 0 , … , x n ] / I .

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

View Paper: https://www.semanticscholar.org/paper/7c72b6219d81e7edcf7e7cacdec5b53df126fc81

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In Algebra and Number Theory

In Computational Theory and Mathematics

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Citations in the corpus

Characteristic-free bounds for the Castelnuovo–Mumford regularity (2003, unknown): “We also recall that monomial ideals which have lexicographic associated prime ideals have been used in [BeGm] for algorithmic computations of the Castelnuovo-Mumford regularity.”
How to compute the Stanley depth of a monomial ideal (2007, background): “joint intervals such that the end point of each interval is at least a 3-set of the poset shown above. If one of these intervals is [i,1234], say [1,1234], then one of the intervals [2,234], [3,234], [4,234] would have to cover the rest, a contradiction. Otherwise we have four disjoint intervals of ”
Edge ideals: algebraic and combinatorial properties (2010, methodology): “There are methods to compute the regularity of R/I avoiding the construction of a minimal graded free resolution, see [3] and [50, p.”