On rank 3 quadratic equations of Veronese embeddings

Euisung Park and Saerom Sim

Mathematische Nachrichten, 2025, vol. 298, issue 9, 3135-3155

Abstract: This paper studies the geometric structure of the locus Φ3(X)$\Phi _3 (X)$ of rank 3 quadratic equations of the Veronese variety X=νd(Pn)$X = \nu _d ({\mathbb {P}}^n)$. Specifically, we investigate the minimal irreducible decomposition of Φ3(X)$\Phi _3 (X)$ of rank 3 quadratic equations and analyze the geometric properties of the irreducible components of Φ3(X)$\Phi _3 (X)$ such as their desingularizations. Additionally, we explore the non‐singularity and singularity of these irreducible components of Φ3(X)$\Phi _3 (X)$.

Date: 2025
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