单项式几乎完全交的合束和弱Lefschetz性质

IF 0.3 4区数学 Q4 MATHEMATICS Journal of Commutative Algebra Pub Date : 2021-06-01 DOI:10.1216/jca.2021.13.157

D. Cook, U. Nagel

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引用次数: 2

摘要

确定弱Lefschetz性质的存在通常是一个具有挑战性的问题。在Brenner and Kaid(2007)、Cook II and Nagel(2011)以及Migliore、micro - roig、Murai and Nagel(2013)的研究基础上，我们对三个变量中的四个发生器的Artinian单项式理想进行了深入研究。我们利用菱形拼接的连接描述了这种理想的合束的半稳定性，确定了它的一般分裂类型，并确定了弱Lefschetz性质的存在。我们给出了特征零和正特征的结果。

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Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections

Deciding the presence of the weak Lefschetz property often is a challenging problem. Continuing studies of Brenner and Kaid (2007), Cook II and Nagel (2011) and Migliore, Miro-Roig, Murai and Nagel (2013) we carry out an in-depth study of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings to describe semistability of the syzygy bundle of such an ideal, to determine its generic splitting type, and to decide the presence of the weak Lefschetz property. We provide results in both characteristic zero and positive characteristic.

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来源期刊

Journal of Commutative Algebra MATHEMATICS-

CiteScore

0.80

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.

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