Amoeba-shaped polyhedral complex of an algebraic hypersurface
arXiv:1708.06870
Abstract
Given a complex algebraic hypersurface~, we introduce a polyhedral complex which is a subset of the Newton polytope of the defining polynomial for~ and enjoys the key topological and combinatorial properties of the amoeba of~ We provide an explicit formula for this polyhedral complex in the case when the spine of the amoeba is dual to a triangulation of the Newton polytope of the defining polynomial. In particular, this yields a description of the polyhedral complex when the hypersurface is optimal.
12 pages, 23 figures