论文标题
长度4大结构的DG结构来自小结构
DG Structure on the Length 4 Big From Small Construction
论文作者
论文摘要
Kustin和Miller引入了小型结构，可用于构建紧密连接的Gorenstein理想的分辨率。在本文中，我们扩展了DG-Elgebra技术引入了Kustin，用于构建矩阵因素化并在长度为4 $的长度上构建DG-Elgebra结构，从小结构中。所采用的技术涉及从泰特式复合物到表现出庞加莱双重性的无环的DG-Elgebra的形态。这引起了同态，经过适当的修改，这些同态满足了一系列身份清单，最终完美地封装了所需的产品结构所需的关联性和DG公理，用于从小结构中。
The big from small construction was introduced by Kustin and Miller and can be used to construct resolutions of tightly double linked Gorenstein ideals. In this paper, we expand on the DG-algebra techniques introduced Kustin for building matrix factorizations and construct a DG-algebra structure on the length $4$ big from small construction. The techniques employed involve the construction of a morphism from a Tate-like complex to an acyclic DG-algebra exhibiting Poincaré duality. This induces homomorphisms which, after suitable modifications, satisfy a list of identities that end up perfectly encapsulating the required associativity and DG axioms of the desired product structure for the big from small construction.
