Generic tropical initial ideals of Cohen-Macaulay algebras |
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| Authors: | Kiumars Kaveh Christopher Manon Takuya Murata |
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| Affiliation: | 1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA;2. Department of Mathematics, University of Kentucky, Lexington, KY, USA;1. Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK;2. Department of Physics, Mathematics and Informatics, National Academy of Sciences of Belarus, 66 Prospekt Nezavisimosti, Minsk, Belarus;1. School of Mathematical Sciences, Harbin Normal University, 150025 Harbin, China;2. School of Mathematics and Statistics, Hainan Normal University, 571158 Haikou, China |
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| 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.” |
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| Keywords: | 14T05 14M05 13A18 |
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