On rank 3 quadratic equations of Veronese varieties
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916538556088320 |
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| author | Park, Euisung Sim, Saerom |
| author_facet | Park, Euisung Sim, Saerom |
| contents | This paper studies the geometric structure of the locus $Φ_3 (X)$ of rank $3$ quadratic equations of the Veronese variety $X = ν_d (\mathbb{P}^n)$. Specifically, we investigate the minimal irreducible decomposition of $Φ_3 (X)$ of rank $3$ quadratic equations and analyze the geometric properties of the irreducible components of $Φ_3 (X)$ such as their desingularizations. Additionally, we explore the non-singularity and singularity of these irreducible components of $Φ_3 (X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16983 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On rank 3 quadratic equations of Veronese varieties Park, Euisung Sim, Saerom Algebraic Geometry This paper studies the geometric structure of the locus $Φ_3 (X)$ of rank $3$ quadratic equations of the Veronese variety $X = ν_d (\mathbb{P}^n)$. Specifically, we investigate the minimal irreducible decomposition of $Φ_3 (X)$ of rank $3$ quadratic equations and analyze the geometric properties of the irreducible components of $Φ_3 (X)$ such as their desingularizations. Additionally, we explore the non-singularity and singularity of these irreducible components of $Φ_3 (X)$. |
| title | On rank 3 quadratic equations of Veronese varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.16983 |