Generic tropical initial ideals of Cohen-Macaulay algebras

Kiumars Kaveh; Christopher Manon; Takuya Murata

doi:10.1016/j.jpaa.2021.106713

Generic tropical initial ideals of Cohen-Macaulay algebras

Kiumars Kaveh, Christopher Manon, Takuya Murata

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Article number	106713
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	11
DOIs	https://doi.org/10.1016/j.jpaa.2021.106713
State	Published - Nov 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Funding

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

Funders	Funder number
Simons Collaboration	587209
National Science Foundation Arctic Social Science Program	DMS-1601303, 714052

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2021.106713

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AB - 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.”

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Generic tropical initial ideals of Cohen-Macaulay algebras

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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