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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149143 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Spinor Varieties and Their Secants / L. Manivel // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862751805945937920 |
|---|---|
| author | Manivel, L. |
| author_facet | Manivel, L. |
| citation_txt | On Spinor Varieties and Their Secants / L. Manivel // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T21:13:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149143 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:13:24Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Manivel, L. 2019-02-19T17:39:22Z 2019-02-19T17:39:22Z 2009 On Spinor Varieties and Their Secants / L. Manivel // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 15 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 14M17; 15A66; 14L35; 14N15 https://nasplib.isofts.kiev.ua/handle/123456789/149143 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. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”.I thank J.M. Landsberg, G. Ottaviani and J. Weyman for useful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Spinor Varieties and Their Secants Article published earlier |
| spellingShingle | On Spinor Varieties and Their Secants Manivel, L. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149143 |
| work_keys_str_mv | AT manivell onspinorvarietiesandtheirsecants |