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On rank 3 quadratic equations of Veronese varieties (2412.16983v1)
Published 22 Dec 2024 in math.AG
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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