Variety of apolar schemes to powers of quadrics

2024/09/20 by Kapustka, Grzegorz, Grzegorz Kapustka, Kristian Ranestad +2
Computer Science · Mathematics · #13E10 #13H10 #14J40 #14J45 #14M99 #14N07 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2409.13352

openalex publication_date 2024/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the variety \rmVAPS_G(q₂³, 10) (resp. \rmVAPS_G(q₃², 10)), a Grassmannian compactification of the variety of finite schemes of length 10 apolar to q₂³ (resp. q₃²), where \q_n = 0\⊂ \mathbb Pⁿ is a smooth quadric hypersurface. In particular, we show that \rmVAPS_G(q₂³, 10) is the tangent developable of a rational normal curve, while \rmVAPS_G(q₃², 10) is reducible with three singular 5-dimensional components.

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