THE AMOEBA DIMENSION OF A LINEAR SPACE

Jan Draisma, Sarah Eggleston, Rudi Pendavingh, Johannes Rau, Chi Ho Yuen

Research output: Contribution to journalArticlepeer-review

Abstract

Given a complex vector subspace V of Cn, the dimension of the amoeba of V ∩(C)n depends only on the matroid that V defines on the ground set {1, . . ., n}. Here we prove that this dimension is given by the minimum of a certain function over all partitions of the ground set, as previously conjectured by Rau. We also prove that this formula can be evaluated in polynomial time.

Original languageEnglish
Pages (from-to)2385-2401
Number of pages17
JournalProceedings of the American Mathematical Society
Volume152
Issue number6
DOIs
StatePublished - 1 Jun 2024

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