The amoeba dimension of a linear space

Jan Draisma; Sarah Eggleston; Rudi Pendavingh; Johannes Rau; Chi Ho Yuen

doi:10.1090/proc/16744

The amoeba dimension of a linear space

Jan Draisma (Corresponding author-nrf), Sarah Eggleston, Rudi Pendavingh, Johannes Rau, Chi Ho Yuen

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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.

Originele taal-2	Engels
Pagina's (van-tot)	2385-2401
Aantal pagina's	17
Tijdschrift	Proceedings of the American Mathematical Society
Volume	152
Nummer van het tijdschrift	6
DOI's	https://doi.org/10.1090/proc/16744
Status	Gepubliceerd - 1 jun. 2024

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© 2024 American Mathematical Society.

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The amoeba dimension of a linear space

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