Secant varieties of Segre-Veronese embeddings of \((\mathbb{P }^1)^r\)

DOI10.1007/s00208-012-0890-1zbMath1275.14041arXiv1105.2136OpenAlexW1732649455MaRDI QIDQ2392792

Elisa Postinghel, Antonio Laface

Publication date: 2 August 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2136

zbMATH Keywords

degenerationdouble pointsecant varietyTerracini's lemmaSegre-Veronese embeddingnon-defective variety

Mathematics Subject Classification ID

Fibrations, degenerations in algebraic geometry (14D06) Divisors, linear systems, invertible sheaves (14C20) Projective techniques in algebraic geometry (14N05) Classical problems, Schubert calculus (14N15)

Related Items (18)

On tangential weak defectiveness and identifiability of projective varieties ⋮ Identifiability for the k-secant variety of the Segre-Veronese varieties ⋮ Set evincing the ranks with respect to an embedded variety (symmetric tensor rank and tensor rank) ⋮ On linear systems of \(\mathbb P^3\) with nine base points ⋮ On the secant varieties of tangential varieties ⋮ Secant varieties of toric varieties arising from simplicial complexes ⋮ Secant varieties of the varieties of reducible hypersurfaces in \(\mathbb{P}^n\) ⋮ Most secant varieties of tangential varieties to Veronese varieties are nondefective ⋮ From non-defectivity to identifiability ⋮ Osculating varieties and their joins: $\mathbb{P}^1\times \mathbb{P}^1$ ⋮ On a notion of toric special linear systems ⋮ On non-secant defectivity of Segre-Veronese varieties ⋮ Linear systems on the blow-up of \((\mathbb{P}^1)^n\) ⋮ Identifiability of rank-3 tensors ⋮ Tangential varieties of Segre-Veronese surfaces are never defective ⋮ On secant dimensions and identifiability of flag varieties ⋮ The Hitchhiker guide to: secant varieties and tensor decomposition ⋮ On secant defectiveness and identifiability of Segre-Veronese varieties

Cites Work

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• A new proof of the Alexander-Hirschowitz interpolation theorem
• On linear systems of curves on rational scrolls
• On the dimensions of secant varieties of Segre-Veronese varieties
• New examples of defective secant varieties of Segre-Veronese varieties
• On the ideals of secant varieties to certain rational varieties
• On the non-defectivity of non weak-defectivity of Segre-Veronese embeddings of products of projective spaces
• Segre-Veronese embeddings of \(\mathbb P^1\times\mathbb P^1\times\mathbb P^1\) and their secant varieties
• Weakly defective varieties
• Standard Classes on the Blow-Up of ℙⁿat Points in Very General Position
• Secant varieties of ℙ¹×⋯×ℙ¹ (𝕟-times) are NOT defective for 𝕟≥5
• Secant dimensions of low-dimensional homogeneous varieties
• About the Defectivity of Certain Segre–Veronese Varieties
• Degenerations of Planar Linear Systems
• Linear systems of plane curves with base points of equal multiplicity

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