The amoeba dimension of a linear space

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 of $V$. Here we prove that this dimension is given by the minimum of a certain function over all partitions $P_1,\dots,P_k$ of the ground set into nonempty parts $P_i$, as previously conjectured by Johannes Rau. We also prove that this formula can be evaluated in polynomial time. This is joint work with Jan Draisma, Rudi Pendavingh, Johannes Rau, and Chi Ho Yuen.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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