On the classification of defective threefolds

2003/12/31 by Luca Chiantini, L. Chiantini, Ciro Ciliberto +3 · 1 citation
Mathematics · #14J30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14J30

paper · pdf · doi:10.48550/arxiv.math/0312518

AMSLaTeX, 30 pages

openalex publication_date 2003/12/31 · arxiv created 2004/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify all irreducible projective threefolds X which are k-defective, i.e. some k-secant variety of X has dimension less than the expected value. This results extends the classical Scorza's classification of the case k=1.

Citations

• Grassmann defectivity à la Terracini

Cited by

• Projective and birational geometry of Grassmannians and other special varieties

Related

• On secant defective varieties, in particular of dimension 4
• Induction for secant varieties of Segre varieties
• Birational geometry of defective varieties
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• On non-projective small resolutions