Abstract
We give a complete description of amoebas and coamoebas of k-dimensional very affine linear spaces in (ℂ*)n. This include an upper bound of their dimension, and we show that if a k-dimensional very affine linear space in (ℂ*)n is generic, then the dimension of its (co)amoeba is equal to min{2k, n}. Moreover, we prove that the volume of its coamoeba is equal to π2k. In addition, if the space is generic and real, then the volume of its amoeba is equal to π2k/2k.
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Nisse, M., Passare, M. (2017). Amoebas and Coamoebas of Linear Spaces. In: Andersson, M., Boman, J., Kiselman, C., Kurasov, P., Sigurdsson, R. (eds) Analysis Meets Geometry. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52471-9_4
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DOI: https://doi.org/10.1007/978-3-319-52471-9_4
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-52469-6
Online ISBN: 978-3-319-52471-9
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