2020/01/22 by Ruddat, Helge, Zharkov, Ilia
#14J80 #14T05 #51D20 #57Q37 #57Q45 #57R52 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2001.08267
We show how to deform the map Log\colon (ℂ^*)n → ℝn such that the image of the complex pair of pants P^∘ ⊂ (ℂ^*)n is the tropical hyperplane by showing an (ambient) isotopy between P^∘ ⊂ (ℂ^*)n and a natural polyhedral subcomplex of the product of the two skeleta S× Σ⊂ A × C of the amoeba A and the coamoeba C of P^∘. This lays the groundwork for having the discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus fibrations.