Variations on Pascal's Theorem
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916478234656768 |
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| author | Ciliberto, Ciro Miranda, Rick |
| author_facet | Ciliberto, Ciro Miranda, Rick |
| contents | In this paper we present a variety of statements that are in the spirit of the famous theorem of Pascal, often referred to as the Mystic Hexagon. We give explicit equations describing the conditions for $d+4$ points to lie on rational normal curves. A collection of problems of Pascal type are considered for quadric surfaces in $\bbP^3$. Finally we reprove, using computer algebra methods, a remarkable theorem of Richmond, Segre, and Brown, for quadrics in $\bbP^4$ containing five general lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variations on Pascal's Theorem Ciliberto, Ciro Miranda, Rick Algebraic Geometry Primary 14H45, 14N05, 14N15, 14N20, 14N25, Secondary 14A25, 14Q15 In this paper we present a variety of statements that are in the spirit of the famous theorem of Pascal, often referred to as the Mystic Hexagon. We give explicit equations describing the conditions for $d+4$ points to lie on rational normal curves. A collection of problems of Pascal type are considered for quadric surfaces in $\bbP^3$. Finally we reprove, using computer algebra methods, a remarkable theorem of Richmond, Segre, and Brown, for quadrics in $\bbP^4$ containing five general lines. |
| title | Variations on Pascal's Theorem |
| topic | Algebraic Geometry Primary 14H45, 14N05, 14N15, 14N20, 14N25, Secondary 14A25, 14Q15 |
| url | https://arxiv.org/abs/2411.07638 |