Singular strata of cuspidal type for the classical discriminant

Defective dual varieties for real spectra

“…The complementary type corresponds to discriminant varieties embedded into the cuspidal locus of X A . This generalizes results of [11], where the cuspidal form first appeared in the special case of n = 1 (when P A (t ) is itself a linear form).…”

“…Let A be algebraic. Consider the case n = 1, which was studied in detail in [11], and where the cuspidal form P A (t ) appeared in this special case. As n = 1 the cuspidal form is, for every m, a non-trivial linear form in t vanishing along some hyperplane in P m−1 .…”

“…gives the coefficients, up to multiplication by a constant, α 12 α 22 (α11 − α 21 + α 12 α 21 − α 11 α 22 ) b = α 12 α 21 (1 − α 12 )(1 − α 21 ) − α 11 α 22 (1 − α 11 )(1 − α 22 ) c = α 11 α 21 (α 12 − α 12 α 21 − α 22 + α 11 α 22 )…”

Singular Points of Complex Algebraic Hypersurfaces

“…It means that z = (32/27, 1024/729) is a cuspidal point of the type (4,3) for the discriminant ∆ ′ . Now we have to study singular types of singular points of the complex curve (13) which are given by Theorem 2:…”

On the Structure of the Classical Discriminant

“…The purpose of this article is to refine some classical results on the structure of facets of the Newton polytope of the discriminant ∆, as well as to study factorization of truncations of the discriminant with respect to the facets. The knowledge of this structure is important in the study of a general algebraic function y = y(a) of roots of the polynomial (1) ( [1,2]). …”