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Skeletons of monomial ideals

✍ Scribed by Jürgen Herzog; Ali Soleyman Jahan; Xinxian Zheng

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
105 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In analogy to the skeletons of a simplicial complex and their Stanley–Reisner ideals we introduce the skeletons of an arbitrary monomial ideal I ⊂ 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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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