The Birational Geometry of Ceva's Theorem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916283839152128 |
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| author | Prince, Thomas |
| author_facet | Prince, Thomas |
| contents | In this article we study Ceva's theorem and its higher-dimensional extensions from the perspective of algebraic and projective geometry. First, we situate the theorem within the study of algebraic surfaces by relating it to the defining equation of a del Pezzo surface of degree six inside the product of three projective lines. Second, by interpreting (higher-dimensional analogues of) Ceva's theorem in terms of projections from projective spaces, we recast these results as matrix completion problems. We use these ideas to offer proofs of some higher-dimensional analogues of Ceva's theorem. This article is written with a nonspecialist audience in mind and we hope that some useful context is provided in the form of remarks in the sections on surfaces for students of algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Birational Geometry of Ceva's Theorem Prince, Thomas Algebraic Geometry 51N15 In this article we study Ceva's theorem and its higher-dimensional extensions from the perspective of algebraic and projective geometry. First, we situate the theorem within the study of algebraic surfaces by relating it to the defining equation of a del Pezzo surface of degree six inside the product of three projective lines. Second, by interpreting (higher-dimensional analogues of) Ceva's theorem in terms of projections from projective spaces, we recast these results as matrix completion problems. We use these ideas to offer proofs of some higher-dimensional analogues of Ceva's theorem. This article is written with a nonspecialist audience in mind and we hope that some useful context is provided in the form of remarks in the sections on surfaces for students of algebraic geometry. |
| title | The Birational Geometry of Ceva's Theorem |
| topic | Algebraic Geometry 51N15 |
| url | https://arxiv.org/abs/2406.08378 |