Gromov–Witten theory and invariants of matroids

Abstract We use techniques from Gromov–Witten theory to construct new invariants of matroids taking value in the Chow groups spaces rational curves permutohedral toric variety. When matroid is realizable by a complex hyperplane arrangement, our coincide with virtual fundamental classes used define logarithmic wonderful models arrangement complements, for any structure supported on boundary. boundary empty, this implies that quantum cohomology ring arrangement’s model combinatorial invariant, i.e., it depends only matroid. divisor maximal, we intersection convert class into balanced weighted fan vector space, having expected dimension. explain how associated completely encoded intersections fan. include number questions whose positive answers would lead well-defined non-realizable matroids.