Singularities of the Secant Variety

2007/12/14 by Pete Vermeire, Vermeire, Pete
Mathematics · #14B05 #14N15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0712.2364

openalex publication_date 2007/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give positivity conditions on the embedding of a smooth variety which guarantee the normality of the secant variety, generalizing earlier results of the author and others. We also give classes of secant varieties satisfying the Hodge conjecture as well as a result on the singular locus of degenerate secant varieties.

Citations

• On the ideals and singularities of secant varieties of Segre varieties

Related

• Singularities of secant varieties
• Singularities of secant varieties from a Hodge theoretic perspective
• Singularities and syzygies of secant varieties of smooth projective varieties
• Arithmetic properties of the first secant variety to a projective variety
• On singular varieties having an extremal secant line