论文标题
希尔伯特方案的开放式封面和列表通过相对标记的基础上的商圈上的圆环
Open Covers and Lex Points of Hilbert schemes over quotient rings via relative marked bases
论文作者
论文摘要
我们介绍了基于准稳定理想的相对明显基础的概念，以及建设性的方法和功能解释，开发了用于研究希尔伯特方案对多项式环的商的计算方法。然后，我们专注于两个应用程序。 第一个具有理论风味，当商环在准稳定的理想上是Cohen-Macaulay时，就会产生希尔伯特方案的明确开放式封面。与相对标记的碱基一起，我们使用适当的变量的一般变化，这些变量可抵御期望，从而保留准稳定理想的结构。 第二个应用具有计算味。当商环是准稳定理想的麦考雷 - lex时，我们研究了希尔伯特方案的Lex点，并找到了光滑和奇异的lex点的示例。
We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods for the study of Hilbert schemes over quotients of polynomial rings. Then we focus on two applications. The first has a theoretical flavour and produces an explicit open cover of the Hilbert scheme when the quotient ring is Cohen-Macaulay on quasi-stable ideals. Together with relative marked bases, we use suitable general changes of variables which preserve the structure of the quasi-stable ideal, against the expectations. The second application has a computational flavour. When the quotient rings are Macaulay-Lex on quasi-stable ideals, we investigate the lex-point of the Hilbert schemes and find examples of both smooth and singular lex-points.
