论文标题
$ \ mathbb p^1 \ times \ mathbb p^2 $中的行工会的ACM属性
The ACM property for unions of lines in $\mathbb P^1 \times \mathbb P^2$
论文作者
论文摘要
本文研究了$ \ mathbb p^1 \ times \ times \ mathbb p^2 $ in $ \ mathbb p^1 \ times \ times \ times \ mathbb p^2 $（不一定会减少），概述了某些Codimension 2的算术Cohen-Macaulay（ACM）属性。我们讨论找到一般表征的一些障碍。然后，我们考虑某些类别的此类曲线，我们解决了两个问题。首先，他们自己什么时候是ACM？其次，在非ACM降低的配置中，是否可以通过合适的功率（即“ fatten”一条线）替换主要（素数）分解的一个组件以使所得的方案ACM？最后，对于我们的类曲线类别，我们通过引入完全V连接的配置的定义，以组合术语来表征本地Cohen-Macaulay属性。我们应用了一些结果，为$ \ mathbb p^3 $中的一组线提供类似的ACM结果。
This paper examines the Arithmetically Cohen-Macaulay (ACM) property for certain codimension 2 varieties in $\mathbb P^1\times \mathbb P^2$ called sets of lines in $\mathbb P^1\times \mathbb P^2$ (not necessarily reduced). We discuss some obstacles to finding a general characterization. We then consider certain classes of such curves, and we address two questions. First, when are they themselves ACM? Second, in a non-ACM reduced configuration, is it possible to replace one component of a primary (prime) decomposition by a suitable power (i.e. to "fatten" one line) to make the resulting scheme ACM? Finally, for our classes of such curves, we characterize the locally Cohen-Macaulay property in combinatorial terms by introducing the definition of a fully v-connected configuration. We apply some of our results to give analogous ACM results for sets of lines in $\mathbb P^3$.
