An Octanomial Model for Cubic Surfaces
Algebraic Geometry
2020-10-21 v3
Abstract
We present a new normal form for cubic surfaces that is well suited for p-adic geometry, as it reveals the intrinsic del Pezzo combinatorics of the 27 trees in the tropicalization. The new normal form is a polynomial with eight terms, written in moduli from the E6 hyperplane arrangement. If such a surface is tropically smooth then its 27 tropical lines are distinct. We focus on explicit computations, both symbolic and p-adic numerical.
Cite
@article{arxiv.1908.06106,
title = {An Octanomial Model for Cubic Surfaces},
author = {Marta Panizzut and Emre Can Sertöz and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1908.06106},
year = {2020}
}
Comments
20 pages; clarified exposition at key points; final version