On the contravariant of homogeneous forms arising from isolated\n hypersurface singularities

2016/08/26 by Alexander Isaev, Isaev, Alexander
Engineering · Mathematics · #14L24 #32S25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1608.07627

openalex publication_date 2016/08/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let mathcal Q_n^d be the vector space of homogeneous forms of degree\nd\≥ 3 on mathbb Cⁿ, with n\≥ 2. The object of our study is the map\n\Φ, introduced in earlier articles by J. Alper, M. Eastwood and the author,\nthat assigns to every form for which the discriminant \Δ does not vanish\nthe so-called associated form lying in the space mathcal Q_n^n(d-2)*.\nThis map is a morphism from the affine variety X_n^d:= f\∈ mathcal\nQ_n^d:\Δ(f)\≠ 0 to the affine space mathcal Q_n^n(d-2)*.\nLetting p be the smallest integer for which the product \Δ^p\Φ\nextends to a morphism from mathcal Q_n^d to mathcal Q_n^n(d-2)*,\none observes that the extended map defines a contravariant of forms in\n mathcal Q_n^d. In the present paper we obtain upper bounds for p thus\nproviding estimates for the contravariant's degree.\n

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