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arXiv · 1703.07620

The Tropical Superpotential For $\mathbb{P}^2$

Thomas Prince
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Abstract

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 $\mathbb{P}^2$.

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Thomas Prince. 2017-03-22. The Tropical Superpotential For $\mathbb{P}^2$. https://arxiv.org/abs/1703.07620

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