swMATH ID: 36391
Software Authors: D. Bunnett, H. Keneshlou
Description: Macaulay2 file DetRepOfCubicDiscriminant.m2: contains supporting codes for the computational proofs in the paper ’Determinantal representations of the cubic discriminant. We compute and study two determinantal representations of the discriminant of a cubic quaternary form. The first representation is the Chow form of the 2-uple embedding of ℙ3 and is computed as the Pfaffian of the Chow form of a rank 2 Ulrich bundle on this Veronese variety. We then consider the determinantal representation described by [E. J. Nanson, Proc. R. Soc. Edinburgh 22, 353–358 (1899; JFM 30.0161.09)]. We investigate the geometric nature of cubic surfaces whose discriminant matrices satisfy certain rank conditions. As a special case of interest, we use certain minors of this matrix to suggest equations vanishing on the locus of k -nodal cubic surfaces
Homepage: https://lematematiche.dmi.unict.it/index.php/lematematiche/article/view/1997
Source Code:  https://github.com/Hanieh14/CubicSurfaces/blob/master/DetRepOfCubicDiscriminant.m2
Dependencies: Macaulay2
Related Software: CubicSurfaces; GitHub; Macaulay2; HomotopyContinuation
Cited in: 2 Documents

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