Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Iarrobino, Anthony¹  McDaniel, Chris²  Seceleanu, Alexandra³ 

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

[2] Endicott Coll, 376 Hale St, Beverly, MA 01915 USA

[3] Univ Nebraska, Dept Math, 203 Avery Hall, Lincoln, NE 68588 USA

关键词: Artinian algebra;    Connected sum;    Gorenstein;    Hilbert function;    Lefschetz property;    Thom class;   

DOI  :  10.1016/j.jpaa.2021.106787

来源: Elsevier

【 摘 要 】

In their paper [1], H. Ananthnarayan, L. Avramov, and W.F. Moore introduced a connected sum construction for local Gorenstein rings A, B over a local Gorenstein ring T, which, in the graded Artinian case, can be viewed as an algebraic analogue of the topological construction of the same name. We give two alternative descriptions of this algebraic connected sum: the first uses algebraic analogues of Thom classes of vector bundles and Gysin homomorphisms, the second is in terms of Macaulay dual generators. We also investigate the extent to which the connected sum of A, B over an Artinian Gorenstein algebra T preserves the weak or strong Lefschetz property, thus providing new classes of rings which satisfy these properties. (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

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