The Weak Lefschetz Property of Whiskered Graphs

被引：0

作者：

Cooper, Susan M. ^{[1
]}

Faridi, Sara ^{[2
]}

Holleben, Thiago ^{[2
]}

Nicklasson, Lisa ^{[3
]}

Van Tuyl, Adam ^{[4
]}

机构：

[1] Univ Manitoba, Dept Math, 520 Machray Hall,186 Dysart Rd, Winnipeg, MB R3T 2N2, Canada

[2] Dalhousie Univ, Dept Math & Stat, 6297 Castine Way,POB 15000, Halifax, NS B3H 4R2, Canada

[3] Malardalen Univ, Div Math & Phys, S-72123 Vasteras, Sweden

[4] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4L8, Canada

来源：

LEFSCHETZ PROPERTIES, SLP-WLP 2022 | 2024年 / 59卷

基金：

瑞典研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

Weak Lefschetz property; Graded Artinian rings; Whiskered graphs; Pseudo-manifolds; COMPLETE-INTERSECTIONS; IDEALS;

D O I：

10.1007/978-981-97-3886-1_5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in degrees 1 and n-1 when the characteristic is not two, where n is the number of vertices in the graph. Moreover, the multiplication is injective in degrees < n/2 when the characteristic is zero, following a proof by Hausel. Our result in the characteristic zero case is optimal in the sense that there are whiskered graphs for which the multiplication maps in all intermediate degrees n/2,..., n - 2 of the associated Artinian algebras fail to have maximal rank, and consequently, the weak Lefschetz property.

引用

页码：97 / 110

页数：14

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