Hilbert Functions and Jordan Type of Perazzo Artinian Algebras

被引:0
作者
Abdallah, Nancy [1 ]
Altafi, Nasrin [2 ,3 ]
De Poi, Pietro [4 ]
Fiorindo, Luca [5 ]
Iarrobino, Anthony [6 ]
Marques, Pedro Macias [7 ]
Mezzetti, Emilia [8 ]
Miro-Roig, Rosa M. [9 ]
Nicklasson, Lisa [10 ]
机构
[1] Univ Boras, Inst Ingenjorsvetenskap, Hgsk Boras, Boras, Sweden
[2] Queens Univ, Dept Math & Stat, Kingston, ON, Canada
[3] Kungliga Tekniska Hgsk KTH, Inst Matemat, Stockholm, Sweden
[4] Univ Udine, Dipartimento Sci Matemat Informat & Fis, Via Sci 206, I-33100 Udine, Italy
[5] Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy
[6] Northeastern Univ, Dept Math, Boston, MA 02115 USA
[7] Univ Evora, Dept Matemat, IFA, CIMA,ECT, Rua Romao Ramalho 59, P-7000671 Evora, Portugal
[8] Univ Trieste, Dipartimento Matemat Informat & Geosci, Via Valerio 12-1, I-34127 Trieste, Italy
[9] Univ Barcelona, Fac Matemat & Informat, Gran Via Corts Catalanes 585, Barcelona 08007, Spain
[10] Malardalens Univ, Avdelningen Matemat & Fys, S-72123 Vasteras, Sweden
来源
LEFSCHETZ PROPERTIES, SLP-WLP 2022 | 2024年 / 59卷
关键词
Perazzo hypersurfaces; Lefschetz properties; Artinian Gorenstein algebras; Hilbert function; Jordan type; HESSIANS;
D O I
10.1007/978-981-97-3886-1_3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smallest possible Hilbert function, we give a description of the possible Jordan types for multiplication by any linear form.
引用
收藏
页码:59 / 80
页数:22
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