Non-Archimedean Coamoebae
Mounir Nisse and Frank Sottile.
The manuscript in pdf.
Non-Archimedean CoamoebaeMounir Nisse and Frank Sottile. |
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A coamoeba is the image of a subvariety of a complex torus under the argument map
to the real torus.
Similarly, a non-archimedean coamoeba is the image of a subvariety of a torus over a
non-archimedean field with complex residue field under an argument map.
The phase tropical variety is the closure of
the image under the pair of maps, tropicalization and
argument.
We describe the structure of non-archimedean coamoebae and phase tropical varieties
in terms of complex coamoebae and their phase limit sets.
The argument map depends upon a section of the
valuation map, and we explain how this choice (mildly) affects the non-archimedean
coamoeba.
We also identify a class of varieties whose non-archimedean coamoebae and phase tropical
varieties are objects from polyhedral combinatorics.
The manuscript in pdf.
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