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The Schl\"afli Fan

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arxiv 1905.11951 v2 pith:KP3GFIDN submitted 2019-05-28 math.CO math.AG

Michael Joswig , Marta Panizzut , Bernd Sturmfels This is my paper · ORCID
classification math.COmath.AG
keywords conestropicalaflicubicschlsurfacesanalysisarticle
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abstract

Smooth tropical cubic surfaces are parametrized by maximal cones in the unimodular secondary fan of the triple tetrahedron. There are $344\, 843 \,867$ such cones, organized into a database of $14\,373\,645$ symmetry classes. The Schl\"afli 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.

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Cited by 1 Pith paper

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  1. An Octanomial Model for Cubic Surfaces

    math.AG 2019-08 conditional novelty 6.0 of 10

    A new sparse octanomial normal form for cubic surfaces is defined, and p-adic tropical smoothness in this family forces the 27 lines to be distinct and defined over Q_p.

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