Skeletons of monomial ideals

Details Skeletons of monomial ideals Skeletons of monomial ideals

2008-02-20

arxiv.org/abs/0802.2769v1

Mathematics

Commutative Algebra

Scientific paper

In analogy to the skeletons of a simplicial complex and their Stanley--Reisner ideals we introduce the skeletons of an arbitrary monomial ideal $I\subset S=K[x_1,...,x_n]$. This allows us to compute the depth of $S/I$ in terms of its skeleton ideals. We apply these techniques to show that Stanley's conjecture on Stanley decompositions of $S/I$ holds provided it holds whenever $S/I$ is Cohen--Macaulay. We also discuss a conjecture of Soleyman-Jahan and show that it suffices to prove his conjecture for monomial ideals with linear resolution.

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