An Octanomial Model for Cubic Surfaces

This page contains the supplementary material for the article:

Marta Panizzut, Emre Can Sertöz, and Bernd Sturmfels: An octanomial model for cubic surfaces

In: Le Matematiche, 75 (2020) 2, p. 517-536

DOI: 10.4418/2020.75.2.8 ARXIV: https://arxiv.org/abs/1908.06106 CODE: https://mathrepo.mis.mpg.de/octanomial

Cubic surfaces are represented by a polynomial with eight terms

\[a \cdot xyz + b \cdot xyw + c \cdot xzw + d \cdot yzw + e \cdot x^2 y + f \cdot x y^2 + g \cdot z^2 w + h \cdot z w^2,\]

with coefficients written in moduli from the \(\textrm{E}_6\) hyperplane arrangement. The codes and outputs of the symbolic and \(p\)-adic numerical computations are presented following the structure of the paper.

• Section 2: Algebra and Combinatorics
• Section 3: Arrangements of Trees
• Section 4: Dense Cubics

The magma codes used to run the computations in Section 4 of the paper can be found in the github repository https://github.com/emresertoz/pAdicCubicSurface.

Project contributors: Marta Panizzut, Emre Can Sertöz, and Bernd Sturmfels

Software used: Magma