Generic tropical initial ideals of Cohen-Macaulay algebras

[摘要] 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 Riimer 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 CohenMacaulay domains are well-poised in codimension 1. (C) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-11-01