Generic initial ideals of Artinian ideals having Lefschetz properties or the strong Stanley property

[摘要] For 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 gin(I). Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of gin(I) are determined just by 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 number of gin(I) is determined by the graded Betti numbers of I if A has the weak Lefschetz property. And if A has the strong Lefschetz (respectively Stanley) property, then we show that the minimal system of generators of gin(I) is determined by the graded Betti numbers (respectively by the Hilbert function) of I. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] generic initial ideal;standard Artinian ideal;Lefschetz property;Stanley property;Hilbert function;graded Betti number;minimal system of generators