On non-secant defectivity of Segre-Veronese varieties

2016/11/05 by Araujo, Carolina, Massarenti, Alex, Rischter, Rick · 1 citation
#14N15 #15A69 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 14N05 #Secondary 14E05

paper · doi:10.48550/arxiv.1611.01674

Abstract

Let SV^{\pmb n}_{\pmb d} be the Segre-Veronese given as the image of the embedding induced by the line bundle O_{ℙⁿ¹×…×ℙ^nr}(d₁,…, d_r). We prove that asymptotically SV^{\pmb n}_{\pmb d} is not h-defective for h≤ n₁^{\lfloor log₂(d-1)\rfloor}.

Cited by

• Osculating Geometry and Higher-Order Distance Loci

Related

• Secant varieties of Segre-Veronese varieties ℙ^m×ℙⁿ embedded by O(1,2) are non-defective for n≫ m³, m≥3
• On secant defectiveness and identifiability of Segre-Veronese varieties
• Secant Varieties of (P ¹) X .... X (P ¹) (n-times) are NOT Defective for n ≥ 5
• Secant varieties of Segre-Veronese embeddings of (P¹)^r
• Higher secant varieties of Segre-Veronese varieties