# String cone and superpotential combinatorics for flag and Schubert varieties in type A

@article{Bossinger2019StringCA, title={String cone and superpotential combinatorics for flag and Schubert varieties in type A}, author={Lara Bossinger and Ghislain Fourier}, journal={J. Comb. Theory, Ser. A}, year={2019}, volume={167}, pages={213-256} }

We study the combinatorics of pseudoline arrangements and their relation to the geometry of flag and Schubert varieties. We associate to each pseudoline arrangement two polyhedral cones, defined in a dual manner. We prove that one of them is the weighted string cone by Littelmann and Berenstein-Zelevinsky. For the other we show how it arises in the framework of cluster varieties and mirror symmetry by Gross-Hacking-Keel-Kontsevich: for the flag variety the cone is the tropicalization of their… Expand

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