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The Schläfli Fan

Joswig, Michael; Panizzut, Marta; Sturmfels, Bernd

Smooth tropical cubic surfaces are parametrized by maximal cones in the unimodular secondary fan of the triple tetrahedron. There are 344843867 such cones, organized into a database of 14373645 symmetry classes. The Schläfli fan gives a further refinement of these cones. It reveals all possible patterns of lines on tropical cubic surfaces, thus serving as a combinatorial base space for the universal Fano variety. This article develops the relevant theory and offers a blueprint for the analysis of big data in tropical geometry.
Published in: Discrete & Computational Geometry, 10.1007/s00454-020-00215-x, Springer Nature