Chow-Lam Recovery
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909642057056256 |
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| author | Pratt, Elizabeth Ranestad, Kristian |
| author_facet | Pratt, Elizabeth Ranestad, Kristian |
| contents | We study the conditions under which a subvariety of the Grassmannian may be recovered from certain of its linear projections. In the special case that our Grassmannian is projective space, this is equivalent to asking when a variety can be recovered from its Chow form; the answer is "always" by work of Chow in 1937. In the general Grassmannian setting, the analogous question is when a variety can be recovered from its Chow-Lam form. We give both necessary conditions for recovery and families of examples where, in contrast with the projective case, recovery is not possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chow-Lam Recovery Pratt, Elizabeth Ranestad, Kristian Algebraic Geometry We study the conditions under which a subvariety of the Grassmannian may be recovered from certain of its linear projections. In the special case that our Grassmannian is projective space, this is equivalent to asking when a variety can be recovered from its Chow form; the answer is "always" by work of Chow in 1937. In the general Grassmannian setting, the analogous question is when a variety can be recovered from its Chow-Lam form. We give both necessary conditions for recovery and families of examples where, in contrast with the projective case, recovery is not possible. |
| title | Chow-Lam Recovery |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.02691 |