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arXiv · 2303.13143

The amoeba dimension of a linear space

Jan Draisma·Sarah Eggleston·Rudi Pendavingh·Johannes Rau·Chi Ho Yuen
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Abstract

Given a complex vector subspace $V$ of $\mathbb{C}^n$, the dimension of the amoeba of $V \cap (\mathbb{C}^*)^n$ depends only on the matroid that $V$ defines on the ground set $\{1,\ldots,n\}$. 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.

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Jan Draisma, Sarah Eggleston, Rudi Pendavingh, Johannes Rau, Chi Ho Yuen. 2023-11-21. The amoeba dimension of a linear space. https://arxiv.org/abs/2303.13143

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