Algebraic surfaces as Hadamard products of curves
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912984045977600 |
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| author | Antolini, Dario Ballico, Edoardo Oneto, Alessandro |
| author_facet | Antolini, Dario Ballico, Edoardo Oneto, Alessandro |
| contents | We study projective surfaces in $\mathbb{P}^3$ which can be written as Hadamard product of two curves. We show that quadratic surfaces which are Hadamard product of two lines are smooth and tangent to all coordinate planes, and such tangency points uniquely identify the quadric. The variety of such quadratic surfaces corresponds to the Zariski closure of the space of symmetric matrices whose inverse has null diagonal. For higher-degree surfaces which are Hadamard product of a line and a curve we show that the intersection with the coordinate planes is always non-transversal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic surfaces as Hadamard products of curves Antolini, Dario Ballico, Edoardo Oneto, Alessandro Algebraic Geometry 14J25, 14M99 We study projective surfaces in $\mathbb{P}^3$ which can be written as Hadamard product of two curves. We show that quadratic surfaces which are Hadamard product of two lines are smooth and tangent to all coordinate planes, and such tangency points uniquely identify the quadric. The variety of such quadratic surfaces corresponds to the Zariski closure of the space of symmetric matrices whose inverse has null diagonal. For higher-degree surfaces which are Hadamard product of a line and a curve we show that the intersection with the coordinate planes is always non-transversal. |
| title | Algebraic surfaces as Hadamard products of curves |
| topic | Algebraic Geometry 14J25, 14M99 |
| url | https://arxiv.org/abs/2502.18813 |