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arXiv · 2409.13352

Variety of apolar schemes to powers of quadrics

Grzegorz Kapustka·Michał Kapustka·Kristian Ranestad
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Abstract

We study the variety $\rm{VAPS}_G(q_2^3, 10)$ (resp. $\rm{VAPS}_G(q_3^2, 10)$), a Grassmannian compactification of the variety of finite schemes of length $10$ apolar to $q_{2}^3$ (resp. $q_3^2$), where $\{q_{n} = 0\}\subset \mathbb P^{n} $ is a smooth quadric hypersurface. In particular, we show that $\rm{VAPS_G}(q_2^3, 10)$ is the tangent developable of a rational normal curve, while $\rm{VAPS}_G(q_3^2, 10)$ is reducible with three singular $5$-dimensional components.

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Grzegorz Kapustka, Michał Kapustka, Kristian Ranestad. 2024-09-20. Variety of apolar schemes to powers of quadrics. https://arxiv.org/abs/2409.13352

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