Geodesic
On discriminants of multilinear forms
Izvestiya. Mathematics , Tome 62 (1998) no. 2, pp. 215-245

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In this paper, an algorithm for calculating the discriminants of multilinear forms is elaborated. A technique is developed for finding the singularity conditions and other invariants for $n$-ary forms. An integral transformation for forms of degree 3 and higher (an analogue of the Gauss transformation for quadratic forms) is introduced. 
@article{IM2_1998_62_2_a0,
     author = {V. V. Dolotin},
     title = {On discriminants of multilinear forms},
     journal = {Izvestiya. Mathematics },
     pages = {215--245},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a0/}
}
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V. V. Dolotin. On discriminants of multilinear forms. Izvestiya. Mathematics , Tome 62 (1998) no. 2, pp. 215-245. http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a0/