The amoeba dimension of a linear space
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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 language | English |
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Journal | Proceedings of the American Mathematical Society |
Volume | 152 |
Issue number | 6 |
Pages (from-to) | 2385-2401 |
Number of pages | 17 |
ISSN | 0002-9939 |
DOIs | |
Publication status | Published - 2024 |
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© 2024 American Mathematical Society.
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