Complete intersection Jordan types in height two

JOURNAL OF ALGEBRA

卷:557

Article

Altafi, Nasrin¹  Iarrobino, Anthony²  Khatami, Leila³ 

[1] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

[2] Northeastern Univ, Dept Math, Boston, MA 02115 USA

[3] Union Coll, Dept Math, Schenectady, NY 12308 USA

关键词: Artinian algebra;    Complete intersection;    Hessian;    Hilbert function;    Hook code;    Jordan type;    Partition;   

DOI  :  10.1016/j.jalgebra.2020.04.015

来源: Elsevier

【 摘 要 】

We determine every Jordan type partition that occurs as the Jordan block decomposition for the multiplication map by a linear form in a height two homogeneous complete intersection (CI) Artinian algebra A over an algebraically closed field k of characteristic zero or large enough. We show that these CI Jordan type partitions are those satisfying specific numerical conditions; also, given the Hilbert function H(A), they are completely determined by which higher Hessians of A vanish at the point corresponding to the linear form. We also show new combinatorial results about such partitions, and in particular we give ways to construct them from a branch label or hook code, showing how branches are attached to a fundamental triangle to form the Ferrers diagram. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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