Connected Sums of Graded Artinian Gorenstein Algebras and Lefschetz Properties
Connected Sums of Graded Artinian Gorenstein Algebras and Lefschetz Properties
复制标题
DOI：
10.1016/j.jpaa.2021.106787
复制
发表时间：
2019-04
期刊：
影响因子：
--
通讯作者：
A. Iarrobino;Chris McDaniel;A. Seceleanu
中科院分区：
文献类型：
--
作者：
A. Iarrobino;Chris McDaniel;A. Seceleanu
H.阿南塔纳拉扬湖Avramov和WF摩尔引入了局部Gorenstein环T上局部Gorenstein环A，B的连通和构造，在分次Artin情形下，它可以被看作是同名拓扑构造的代数模拟。我们给出了两种不同的描述，这个代数连接和：第一个使用代数类似物的Thom类向量丛和Gysin同态，第二个是在麦考利双发电机。我们还研究了Artin Gorenstein代数T上A，B的连通和在多大程度上保持弱或强Lefschetz性质，从而提供了满足这些性质的新的环类.
Abstract In their paper [1], H. Ananthnarayan, L. Avramov, and WF 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.