Preprint 41/2019

The Schläfli Fan

Michael Joswig, Marta Panizzut, and Bernd Sturmfels

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Submission date: 29. May. 2019
Bibtex
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
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 the 27 or more 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 algebraic geometry. We conclude with a sparse model for cubic surfaces over a field with valuation.

04.09.2019, 14:40