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.
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页码：97 / 110
页数：14
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