The Newton polytope of the discriminant of a quaternary cubic form

We determine the \(166\,104\) extremal monomials of the discriminant of a quaternary cubic form. These are in bijection with \(D\)-equivalence classes of regular triangulations of the \(3\)-dilated tetrahedron. We describe how to compute these triangulations and their \(D\)-equivalence classes in or...

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Bibliographic Details
Published in:arXiv.org 2019-09
Main Authors: Kastner, Lars, Loewe, Robert
Format: Article
Language:English
Subjects:
Algorithms
Computation
Equivalence
Polytopes
Tetrahedra
Online Access:Get full text
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Summary:We determine the \(166\,104\) extremal monomials of the discriminant of a quaternary cubic form. These are in bijection with \(D\)-equivalence classes of regular triangulations of the \(3\)-dilated tetrahedron. We describe how to compute these triangulations and their \(D\)-equivalence classes in order to arrive at our main result. The computation poses several challenges, such as dealing with the sheer amount of triangulations effectively, as well as devising a suitably fast algorithm for computation of a \(D\)-equivalence class.
ISSN:2331-8422