Generic tropical initial ideals of Cohen-Macaulay algebras

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...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 225; no. 11; p. 106713
Main Authors Kaveh, Kiumars, Manon, Christopher, Murata, Takuya
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2021
Subjects
14M05
13A18
14T05
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Summary: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.”
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2021.106713