论文标题
单一理想及其Artinian减少的细胞分辨率
Cellular resolutions of monomial ideals and their Artinian reductions
论文作者
论文摘要
我们在本文中提出的问题是：哪些单一理想具有最小的细胞分辨率，即通过使CW-复合物的链图获得的最小分辨率？ Velasco为单一理想的示例提供了最少的细胞分辨率，但是这些例子具有很大的生成集。在本文中，我们表明，如果单一理想最多具有四个发电机，那么理想及其（单一的）Artinian减少的细胞分辨率最少。当理想是由两个单元产生的时，我们可以精确描述CW复合物，从而支持理想及其Artinian还原的最小自由分辨率。同样，在这种情况下，我们计算了多面的betti数字，Cohen-Macaulay类型，并确定何时相应的代数为级别代数。
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-complexes? Velasco gave families of examples of monomial ideals that do not have minimal cellular resolutions, but those examples have large minimal generating sets. In this paper, we show that if a monomial ideal has at most four generators, then the ideal and its (monomial) Artinian reductions have minimal cellular resolutions. When the ideal is generated by two monomials, we can give a precise description of the CW-complex supporting minimal free resolution of the ideal and its Artinian reduction. Also, in this case, we compute the multigraded Betti numbers, Cohen-Macaulay type and determine when the corresponding algebra is a level algebra.
