论文标题
CW复合Nagata理想化
CW-complex Nagata Idealizations
论文作者
论文摘要
我们介绍了一种新颖的结构，使我们能够确定CW-Complex $ P（M）$的骨骼元素和$ M $变量的单元。由此，我们可以推断出有限的$ P（m）$的有限CW-SUBPLEXE之间是有限的简单复合物的商，以及一些大型标准的Artinian Gorenstein代数，在\ cite {f：s}中概括了先前的结构{f：s}，\ cite {cgim} {cgim} and { 我们将其应用于Nagata理想化对级代数的概括。这些代数是标准分级的Artinian代数，其Macaulay双发生器被明确地作为Bidegree $（1，D）$的大型多项式。我们考虑与相同类型的Bidegree $（D_1，D_2）$的多项式相关的代数。
We introduce a novel construction which allows us to identify the elements of the skeletons of a CW-complex $P(m)$ and the monomials in $m$ variables. From this, we infer that there is a bijection between finite CW-subcomplexes of $P(m)$, which are quotients of finite simplicial complexes, and some bigraded standard Artinian Gorenstein algebras, generalizing previous constructions in \cite{F:S}, \cite{CGIM} and \cite{G:Z}. We apply this to a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicitly as a bigraded polynomial of bidegree $(1,d)$. We consider the algebra associated to polynomials of the same type of bidegree $(d_1,d_2)$.
