论文标题
Cohen-Macaulay代数的通用热带初始理想
Generic tropical initial ideals of Cohen-Macaulay algebras
论文作者
论文摘要
我们在代数封闭的字段$ \ mathbf {k} $上研究了积极分级的Cohen-Macaulay代数$ r $的通用热带初始理想。在Römer和Schmitz的工作的基础上，我们为每个初始理想提供了一个公式，并以某些$ i $ aidic的过滤表示相关的绝对化。作为推论，我们表明，如果$ r $是一个域，则来自Tropical品种的Codimension-$ 1 $骨架的每个初始理想是PREME的，因此“ Cohen-Macaulay域的通用演示都以编码率良好，以Codimension-codimension-$ 1 $。”
We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra $R$ over an algebraically closed field $\mathbf{k}$. Building on work of Römer and Schmitz, we give a formula for each initial ideal, and we express the associated quasivaluations in terms of certain $I$-adic filtrations. As a corollary, we show that in the case that $R$ is a domain, every initial ideal coming from the codimension-$1$ skeleton of the tropical variety is prime, so "generic presentations of Cohen-Macaulay domains are well-poised in codimension-$1$."
