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arXiv · 2412.16983

On rank 3 quadratic equations of Veronese varieties

Euisung Park·Saerom Sim
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Abstract

This paper studies the geometric structure of the locus $\Phi_3 (X)$ of rank $3$ quadratic equations of the Veronese variety $X = \nu_d (\mathbb{P}^n)$. Specifically, we investigate the minimal irreducible decomposition of $\Phi_3 (X)$ of rank $3$ quadratic equations and analyze the geometric properties of the irreducible components of $\Phi_3 (X)$ such as their desingularizations. Additionally, we explore the non-singularity and singularity of these irreducible components of $\Phi_3 (X)$.

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Euisung Park, Saerom Sim. 2024-12-22. On rank 3 quadratic equations of Veronese varieties. https://arxiv.org/abs/2412.16983

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