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A dimension formula for the nucleus of a Veronese variety

✍ Scribed by Johannes Gmainer; Hans Havlicek

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
95 KB
Volume
305
Category
Article
ISSN
0024-3795

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✦ Synopsis

The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty. We present an explicit formula for the dimension of this nucleus for arbitrary characteristic of the ground field. As a corollary, we obtain a dimension formula for that subspace in the tth symmetric power of a finite-dimensional vector space V which is spanned by the powers a t with a ∈ V.

πŸ“œ SIMILAR VOLUMES

The Projective Noether Maple Package: Co
The Projective Noether Maple Package: Computing the Dimension of a Projective Variety
✍ Marc Giusti; Klemens HΓ€gele; GrΓ©goire Lecerf; JoΓ«l Marchand; Bruno Salvy πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 359 KB

Recent theoretical advances in elimination theory use straight-line programs as a data structure to represent multivariate polynomials. We present here the Projective Noether Package which is a Maple implementation of one of these new algorithms, yielding as a byproduct a computation of the dimensio