Generic Initial Ideals of Artinian Ideals Having Lefschetz Properties or The Strong Stanley Property

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dc.creatorAhn, Jea Man
dc.creatorCho, Young Hyun
dc.creatorPark, Jung Pil
dc.date2006-10-24
dc.date.accessioned2026-07-07T07:29:23Z
dc.date.available2026-07-07T07:29:23Z
dc.descriptionFor a standard Artinian $k$-algebra $A=R/I$, we give equivalent conditions for $A$ to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of the generic initial ideal $\mathrm{gin}(I)$ of $I$ under the reverse lexicographic order. Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of $\mathrm{gin}(I)$ are determined just by the the Hilbert function of $I$ if $A$ has the weak Lefschetz property. Furthermore, for the case that $A$ is a standard Artinian $k$-algebra of codimension 3, we show that every graded Betti numbers of $\mathrm{gin}(I)$ are determined by the graded Betti numbers of $I$ if $A$ has the weak Lefschetz property. And if $A$ has the strong Lefschetz (resp. Stanley) property, then we show that the minimal system of generators of $\mathrm{gin}(I)$ is determined by the graded Betti numbers (resp. by the Hilbert function) of $I$.
dc.identifierhttps://arxiv.org/abs/math/0610733
dc.identifierhttp://arxiv.org/abs/math/0610733
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118089
dc.subjectCommutative Algebra
dc.subject13A02, 13C05, 13D40, 13E10, 13P10
dc.titleGeneric Initial Ideals of Artinian Ideals Having Lefschetz Properties or The Strong Stanley Property
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