DetRepOfCubicDiscriminant.m2
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 2uple 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
