On the classification of certain geproci sets
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909179358216192 |
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| author | Chiantini, Luca Farnik, Lucja Favacchio, Giuseppe Harbourne, Brian Migliore, Juan Szemberg, Tomasz Szpond, Justyna |
| author_facet | Chiantini, Luca Farnik, Lucja Favacchio, Giuseppe Harbourne, Brian Migliore, Juan Szemberg, Tomasz Szpond, Justyna |
| contents | In this short note we develop new methods toward the ultimate goal of classifying geproci sets in $\mathbb P^3$. We apply these methods to show that among sets of $16$ points distributed evenly on $4$ skew lines, up to projective equivalence there are only two distinct geproci sets. We give different geometric distinctions between these sets. The methods we develop here can be applied in a more general set-up; this is the context of the follow-up work arXiv:2308.00761. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16263 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the classification of certain geproci sets Chiantini, Luca Farnik, Lucja Favacchio, Giuseppe Harbourne, Brian Migliore, Juan Szemberg, Tomasz Szpond, Justyna Algebraic Geometry Combinatorics 14M05 and 14M10 and 14N05 and 14N20 In this short note we develop new methods toward the ultimate goal of classifying geproci sets in $\mathbb P^3$. We apply these methods to show that among sets of $16$ points distributed evenly on $4$ skew lines, up to projective equivalence there are only two distinct geproci sets. We give different geometric distinctions between these sets. The methods we develop here can be applied in a more general set-up; this is the context of the follow-up work arXiv:2308.00761. |
| title | On the classification of certain geproci sets |
| topic | Algebraic Geometry Combinatorics 14M05 and 14M10 and 14N05 and 14N20 |
| url | https://arxiv.org/abs/2303.16263 |