On the secant varieties to the tangential varieties of a Veronesean

DOI10.1090/S0002-9939-01-06251-7zbMath0990.14021OpenAlexW1780038108MaRDI QIDQ2781243

Anthony V. Geramita, Maria Virginia Catalisano, Alessandro Gimigliano

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06251-7

zbMATH Keywords

Hilbert functionssecant varietiesinfinitesimal neighbourhoodsJFM 42.0673.02tangent varietiesVeronesean varieties

Mathematics Subject Classification ID

Determinantal varieties (14M12) Classical problems, Schubert calculus (14N15) Infinitesimal methods in algebraic geometry (14B10)

Related Items

Strict inclusions of high rank loci, On the secant varieties of tangential varieties, Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety, Waring-like decompositions of polynomials. I., Most secant varieties of tangential varieties to Veronese varieties are nondefective, Osculating varieties and their joins: $\mathbb{P}^1\times \mathbb{P}^1$, On the secant varieties to the osculating variety of a Veronese surface, Waring, tangential and cactus decompositions, A Terracini lemma for osculating spaces with applications to Veronese surfaces, On the secant varieties to the tangent developable of a Veronese variety, Moment Ideals of Local Dirac Mixtures, Secant varieties to osculating varieties of Veronese embeddings of \(\mathbb P^n\), Tangential varieties of Segre-Veronese surfaces are never defective, Algebraic stories from one and from the other pockets, All secant varieties of the Chow variety are nondefective for cubics and quaternary forms, Symmetric tensor rank with a tangent vector: a generic uniqueness theorem, Higher secant varieties of the Segre varieties \(\mathbb P^1\times\dots\times\mathbb P^1\), The Hitchhiker guide to: secant varieties and tensor decomposition, Ranks of tensors, secant varieties of Segre varieties and fat points

Uses Software

• CoCoA

Cites Work

• La methode d'Horace pour l'interpolation à plusieurs variables
• Chordal varieties of Veronese varieties and catalecticant matrices
• Some features of \(CoCoA 3\)
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• Joins and higher secant varieties.
• Varieties of sums of power
• The Possible Dimensions of the Higher Secant Varieties
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