The Schl\"afli Fan
Combinatorics
2021-08-03 v2 Algebraic Geometry
Abstract
Smooth tropical cubic surfaces are parametrized by maximal cones in the unimodular secondary fan of the triple tetrahedron. There are such cones, organized into a database of 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.
Keywords
Cite
@article{arxiv.1905.11951,
title = {The Schl\"afli Fan},
author = {Michael Joswig and Marta Panizzut and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1905.11951},
year = {2021}
}
Comments
Major revision: improved presentation and Section 7 deleted