We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra R over an algebraically closed field 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.”

中文翻译：

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Cohen-Macaulay代数的一般热带初始理想

我们研究了代数封闭域k上正分数Cohen-Macaulay代数R的一般热带初始理想。在罗默（Römer）和施密茨（Schmitz）的工作的基础上，我们给出了每个初始理想的公式，并根据某些I- adic过滤表达了相关的准评估。作为推论，我们证明在R是一个域的情况下，来自热带变种的codimension 1骨架的每个初始理想都是素数，因此“ Cohen-Macaulay域的一般表示在codimension 1中是很好的平衡”。