Finite sets of points in $\mathbb{P}^4$ with special projection properties
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911940100489216 |
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| author | Chiantini, Luca Farnik, Łucja Favacchio, Giuseppe Harbourne, Brian Migliore, Juan Szemberg, Tomasz Szpond, Justyna |
| author_facet | Chiantini, Luca Farnik, Łucja Favacchio, Giuseppe Harbourne, Brian Migliore, Juan Szemberg, Tomasz Szpond, Justyna |
| contents | In this note we introduce the notion of $(b,d)$-geprofi sets and study their basic properties. These are sets of $bd$ points in $\mathbb{P}^4$ whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree $b$ and a surface of degree $d$. We show that such nontrivial sets exist if and only if $b\geq 4$ and $d\geq 2$. Somewhat surprisingly, for infinitely many values of $b$ and $d$ there exist such sets in linear general position. The note contains open questions and problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_01744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite sets of points in $\mathbb{P}^4$ with special projection properties Chiantini, Luca Farnik, Łucja Favacchio, Giuseppe Harbourne, Brian Migliore, Juan Szemberg, Tomasz Szpond, Justyna Algebraic Geometry Commutative Algebra Combinatorics 14N05, 14C17, 14N20, 14M10, 14M05, 14M07, 13C40, 05E14 In this note we introduce the notion of $(b,d)$-geprofi sets and study their basic properties. These are sets of $bd$ points in $\mathbb{P}^4$ whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree $b$ and a surface of degree $d$. We show that such nontrivial sets exist if and only if $b\geq 4$ and $d\geq 2$. Somewhat surprisingly, for infinitely many values of $b$ and $d$ there exist such sets in linear general position. The note contains open questions and problems. |
| title | Finite sets of points in $\mathbb{P}^4$ with special projection properties |
| topic | Algebraic Geometry Commutative Algebra Combinatorics 14N05, 14C17, 14N20, 14M10, 14M05, 14M07, 13C40, 05E14 |
| url | https://arxiv.org/abs/2407.01744 |