The amoeba dimension of a linear space

2023/03/23 by Draisma, Jan, Eggleston, Sarah, Pendavingh, Rudi +2 · 1 citation
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.13143

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.

Cited by

• Dilworth truncations and Hadamard products of linear spaces

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