论文标题
Peeva和Srinivasan的DG产品一致
The DG Products of Peeva and Srinivasan Coincide
论文作者
论文摘要
考虑理想的$（x_1，\ dotsc，x_n）^d \ subseteq k [x_1，\ dotsc，x_n] $，其中$ k $是任何字段。 Buchsbaum和Eisenbud的$ L $复合物以及Eliahou-Kervaire的解决方案都可以解决这个理想。这两种复合物都承认了关联DG代数的结构，这是Peeva的问题，即这些DG结构一般是否重合。在本文中，我们在上述复合物之间构建了复合物的同构，这也是代数与其各自产品的同构，从而对Peeva的问题给出了肯定的答案。
Consider the ideal $(x_1 , \dotsc , x_n)^d \subseteq k[x_1 , \dotsc , x_n]$, where $k$ is any field. This ideal can be resolved by both the $L$-complexes of Buchsbaum and Eisenbud, and the Eliahou-Kervaire resolution. Both of these complexes admit the structure of an associative DG algebra, and it is a question of Peeva as to whether these DG structures coincide in general. In this paper, we construct an isomorphism of complexes between the aforementioned complexes that is also an isomorphism of algebras with their respective products, thus giving an affirmative answer to Peeva's question.
