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