ScalingStacks

Theorem (Kapranov [ 7 ] ) . [04T4]

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Theorem (Kapranov [7]).

If VK⊂(K∗)n+1V_{K}\subset(K^{*})^{n+1} is a hypersurface given by a polynomial f=∑aj​zjf=\sum a_{j}z^{j}, aj∈K∗a_{j}\in K^{*} then the (non-Archimedian) amoeba of VKV_{K} is a balanced polyhedral complex corresponding to the function v⁡(j)=val⁡(aj)v(j)=\operatorname{val}(a_{j}) defined on the lattice points of the Newton polyhedron Δ\Delta of VKV_{K} as in Example 2.

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