2017/03/22 by Thomas Prince, Prince, Thomas
Mathematics · #14J33 #14J45 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:14J33 #msc:14J45
paper · pdf · doi:10.48550/arxiv.1703.07620
28 pages, 15 figures. Substantially revised with considerably more detailed arguments and several new figures
arxiv created 2019/02/06 · arxiv updated 2019/02/07
We present an extended worked example of the computation of the tropical superpotential considered by Carl--Pumperla--Siebert. In particular we consider an affine manifold associated to the complement of a non-singular genus one plane curve, and calculate the wall and chamber decomposition determined by the Gross--Siebert algorithm. Using the results of Carl--Pumperla--Siebert we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, which we demonstrate to be identical to the Laurent polynomials predicted by Coates--Corti--Galkin--Golyshev--Kaspzryk to be mirror to ℙ2.