Generic tropical initial ideals of Cohen-Macaulay algebras

Kiumars Kaveh, Christopher Manon, Takuya Murata

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.”

Original languageEnglish
Article number106713
JournalJournal of Pure and Applied Algebra
Volume225
Issue number11
DOIs
StatePublished - Nov 2021

Bibliographical note

Funding Information:
The second author is partially supported by a Simons Collaboration Grant for Mathematicians (Award Number: 587209) .

Funding Information:
The first author is partially supported by a National Science Foundation Grant (Grant ID: DMS-1601303 ) and a Simons Collaboration Grant for Mathematicians (Award Number: 714052 ).

Publisher Copyright:
© 2021 Elsevier B.V.

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Generic tropical initial ideals of Cohen-Macaulay algebras'. Together they form a unique fingerprint.

Cite this