Mapping toric varieties into low dimensional spaces
A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then any d-dimensional projective variety can be mapped...
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| Format: | Article |
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American Mathematical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/51994/ |
| _version_ | 1848798622274027520 |
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| author | Dufresne, Emilie Jeffries, Jack |
| author_facet | Dufresne, Emilie Jeffries, Jack |
| author_sort | Dufresne, Emilie |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then any d-dimensional projective variety can be mapped injectively to 2d + 1-dimensional projective space. A natural question then arises: what is the minimal m such that a projective variety can be mapped injectively to m-dimensional projective space? In this paper we investigate this question for normal toric varieties, with our most complete results being for Segre-Veronese varieties. |
| first_indexed | 2025-11-14T20:22:42Z |
| format | Article |
| id | nottingham-51994 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:22:42Z |
| publishDate | 2016 |
| publisher | American Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-519942020-05-04T18:00:36Z https://eprints.nottingham.ac.uk/51994/ Mapping toric varieties into low dimensional spaces Dufresne, Emilie Jeffries, Jack A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then any d-dimensional projective variety can be mapped injectively to 2d + 1-dimensional projective space. A natural question then arises: what is the minimal m such that a projective variety can be mapped injectively to m-dimensional projective space? In this paper we investigate this question for normal toric varieties, with our most complete results being for Segre-Veronese varieties. American Mathematical Society 2016-07-19 Article PeerReviewed Dufresne, Emilie and Jeffries, Jack (2016) Mapping toric varieties into low dimensional spaces. Transactions of the American Mathematical Society . ISSN 1088-6850 (In Press) Segre-Veronese varieties; Dimension of secant variety; Torus invariants; Separating invariants; Local cohomology doi:10.1090/tran/7026 doi:10.1090/tran/7026 |
| spellingShingle | Segre-Veronese varieties; Dimension of secant variety; Torus invariants; Separating invariants; Local cohomology Dufresne, Emilie Jeffries, Jack Mapping toric varieties into low dimensional spaces |
| title | Mapping toric varieties into low dimensional spaces |
| title_full | Mapping toric varieties into low dimensional spaces |
| title_fullStr | Mapping toric varieties into low dimensional spaces |
| title_full_unstemmed | Mapping toric varieties into low dimensional spaces |
| title_short | Mapping toric varieties into low dimensional spaces |
| title_sort | mapping toric varieties into low dimensional spaces |
| topic | Segre-Veronese varieties; Dimension of secant variety; Torus invariants; Separating invariants; Local cohomology |
| url | https://eprints.nottingham.ac.uk/51994/ https://eprints.nottingham.ac.uk/51994/ |