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.”
|Journal of Pure and Applied Algebra
|Published - Nov 2021
Bibliographical noteFunding Information:
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 ).
© 2021 Elsevier B.V.
ASJC Scopus subject areas
- Algebra and Number Theory