Birational geometry of defective varieties, II

2020/10/21 by Edoardo Ballico, Ballico, Edoardo, Claudio Fontanari +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2010.10807

openalex publication_date 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X ⊂ ℙ^r be smooth and irreducible and for k ≥ 0 let ν_k(X) (resp., δ_k(X)) be the k-th contact (resp., the k-th secant) defect of X. For all k ≥ 0 we have the inequality ν_k(X) ≥ δ_k(X) and in the case k=1 we characterize projective varieties X for which equality holds, dim Sing(X) ≤ δ₁(X) -1 and the generic tangential contact locus is reducible.

Related

• Birational geometry of defective varieties
• Projective and birational geometry of Grassmannians and other special varieties
• Singular contact varieties
• On tangential weak defectiveness and identifiability of projective\n varieties
• On Degenerate Secant and Tangential Varieties and Local Differential Geometry