Title: Real Tropical Singularities and Bergman Fans
Abstract:In this paper, we classify singular real plane tropical curves by means of subdivisions of Newton polytopes. First, we introduce signed Bergman fans (generalizing positive Bergman fans from [AKW06]) t...In this paper, we classify singular real plane tropical curves by means of subdivisions of Newton polytopes. First, we introduce signed Bergman fans (generalizing positive Bergman fans from [AKW06]) that describe real tropicalizations of real linear spaces ([Tab15]). Then, we establish a duality of real plane tropical curves and signed regular subdivisions of the Newton polytope and explore the combinatorics. We define a signed secondary fan that parametrizes real tropical Laurent polynomials and study the subset providing singular real plane tropical curves. A cone of the signed secondary fan is of maximal dimensional type if its corresponding subdivision contains only marked points ([MMS12a]). These cones parametrize real plane tropical curves. We classify singular real plane tropical curves of maximal dimensional type.Read More
Publication Year: 2018
Publication Date: 2018-08-23
Language: en
Type: preprint
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Cited By Count: 1
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