On Spinor Varieties and Their Secants
We study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type Dn, cubic equations exist if and only if n ≥ 9. In general the ideal has generators in degrees at least three and four. Finally we observe that the other Freudenthal varieties...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-07-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.078 |
| _version_ | 1818980116357709824 |
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| author | Laurent Manivel |
| author_facet | Laurent Manivel |
| author_sort | Laurent Manivel |
| collection | DOAJ |
| description | We study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type Dn, cubic equations exist if and only if n ≥ 9. In general the ideal has generators in degrees at least three and four. Finally we observe that the other Freudenthal varieties exhibit strikingly similar behaviors. |
| first_indexed | 2024-12-20T17:10:19Z |
| format | Article |
| id | doaj.art-33fe383f13aa40e584cc6264a080660e |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-20T17:10:19Z |
| publishDate | 2009-07-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-33fe383f13aa40e584cc6264a080660e2022-12-21T19:32:09ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-07-015078On Spinor Varieties and Their SecantsLaurent ManivelWe study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type Dn, cubic equations exist if and only if n ≥ 9. In general the ideal has generators in degrees at least three and four. Finally we observe that the other Freudenthal varieties exhibit strikingly similar behaviors.http://dx.doi.org/10.3842/SIGMA.2009.078spinor varietyspin representationsecant varietyFreudenthal variety |
| spellingShingle | Laurent Manivel On Spinor Varieties and Their Secants Symmetry, Integrability and Geometry: Methods and Applications spinor variety spin representation secant variety Freudenthal variety |
| title | On Spinor Varieties and Their Secants |
| title_full | On Spinor Varieties and Their Secants |
| title_fullStr | On Spinor Varieties and Their Secants |
| title_full_unstemmed | On Spinor Varieties and Their Secants |
| title_short | On Spinor Varieties and Their Secants |
| title_sort | on spinor varieties and their secants |
| topic | spinor variety spin representation secant variety Freudenthal variety |
| url | http://dx.doi.org/10.3842/SIGMA.2009.078 |
| work_keys_str_mv | AT laurentmanivel onspinorvarietiesandtheirsecants |