The Newton polytope of the discriminant of a quaternary cubic form
Abstract
We determine the 166104 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 number of triangulations effectively, as well as devising a suitably fast algorithm for computation of a D-equivalence class.
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