TY - JOUR
T1 - Generic tropical initial ideals of Cohen-Macaulay algebras
AU - Kaveh, Kiumars
AU - Manon, Christopher
AU - Murata, Takuya
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/11
Y1 - 2021/11
N2 - 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.”
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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U2 - 10.1016/j.jpaa.2021.106713
DO - 10.1016/j.jpaa.2021.106713
M3 - Article
AN - SCOPUS:85102036329
SN - 0022-4049
VL - 225
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 11
M1 - 106713
ER -