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On rank 3 quadratic equations of Veronese embeddings

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  • Euisung Park
  • Saerom Sim

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)$\Phi _3 (X)$.

Suggested Citation

  • Euisung Park & Saerom Sim, 2025. "On rank 3 quadratic equations of Veronese embeddings," Mathematische Nachrichten, Wiley Blackwell, vol. 298(9), pages 3135-3155, September.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:9:p:3135-3155
    DOI: 10.1002/mana.70028
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