Higher order duality and toric embeddings
- Autores
- Dickenstein, Alicia Marcela; di Rocco, Sandra; Piene, Ragni
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety.
La notion de variété duale d’ordre supérieur d’une variété projective, introduite par Piene en 1983, est une généralisation naturelle de la notion classique de dualité projective. Dans cet article, nous étudions les variétés duales d’ordre supérieur d’une immersion torique projective. Nous exprimons le degré de la variété duale d’ordre 2 d’une immersion 2-jet régulière, lisse et de dimension 3 en termes géometriques et combinatoires, et nous donnons une classification des variétés ayant une variété duale d’ordre 2 de dimension plus petite qu’attendu. Nous décrivons aussi la tropicalisation des variétés duales de tout ordre d’une variété torique immersée de façon équivariante (pas nécessairement normale).
Fil: Dickenstein, Alicia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: di Rocco, Sandra. Royal Institute Of Technology; Suecia
Fil: Piene, Ragni. University Of Oslo; Noruega - Materia
-
Higher dual variety
Toric variety
Tropicalization
Degree - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19058
Ver los metadatos del registro completo
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Higher order duality and toric embeddingsDualité d’ordre supérieur et immersions toriquesDickenstein, Alicia Marceladi Rocco, SandraPiene, RagniHigher dual varietyToric varietyTropicalizationDegreehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety.La notion de variété duale d’ordre supérieur d’une variété projective, introduite par Piene en 1983, est une généralisation naturelle de la notion classique de dualité projective. Dans cet article, nous étudions les variétés duales d’ordre supérieur d’une immersion torique projective. Nous exprimons le degré de la variété duale d’ordre 2 d’une immersion 2-jet régulière, lisse et de dimension 3 en termes géometriques et combinatoires, et nous donnons une classification des variétés ayant une variété duale d’ordre 2 de dimension plus petite qu’attendu. Nous décrivons aussi la tropicalisation des variétés duales de tout ordre d’une variété torique immersée de façon équivariante (pas nécessairement normale).Fil: Dickenstein, Alicia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: di Rocco, Sandra. Royal Institute Of Technology; SueciaFil: Piene, Ragni. University Of Oslo; NoruegaAnnales Inst Fourier2014-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19058Dickenstein, Alicia Marcela; di Rocco, Sandra; Piene, Ragni; Higher order duality and toric embeddings; Annales Inst Fourier; Annales de L Institut Fourier; 64; 1; 8-2014; 375-4000373-0956CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1111.4641info:eu-repo/semantics/altIdentifier/doi/10.5802/aif.2851info:eu-repo/semantics/altIdentifier/url/http://aif.cedram.org/item?id=AIF_2014__64_1_375_0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:06Zoai:ri.conicet.gov.ar:11336/19058instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:51:07.104CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Higher order duality and toric embeddings Dualité d’ordre supérieur et immersions toriques |
title |
Higher order duality and toric embeddings |
spellingShingle |
Higher order duality and toric embeddings Dickenstein, Alicia Marcela Higher dual variety Toric variety Tropicalization Degree |
title_short |
Higher order duality and toric embeddings |
title_full |
Higher order duality and toric embeddings |
title_fullStr |
Higher order duality and toric embeddings |
title_full_unstemmed |
Higher order duality and toric embeddings |
title_sort |
Higher order duality and toric embeddings |
dc.creator.none.fl_str_mv |
Dickenstein, Alicia Marcela di Rocco, Sandra Piene, Ragni |
author |
Dickenstein, Alicia Marcela |
author_facet |
Dickenstein, Alicia Marcela di Rocco, Sandra Piene, Ragni |
author_role |
author |
author2 |
di Rocco, Sandra Piene, Ragni |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Higher dual variety Toric variety Tropicalization Degree |
topic |
Higher dual variety Toric variety Tropicalization Degree |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety. La notion de variété duale d’ordre supérieur d’une variété projective, introduite par Piene en 1983, est une généralisation naturelle de la notion classique de dualité projective. Dans cet article, nous étudions les variétés duales d’ordre supérieur d’une immersion torique projective. Nous exprimons le degré de la variété duale d’ordre 2 d’une immersion 2-jet régulière, lisse et de dimension 3 en termes géometriques et combinatoires, et nous donnons une classification des variétés ayant une variété duale d’ordre 2 de dimension plus petite qu’attendu. Nous décrivons aussi la tropicalisation des variétés duales de tout ordre d’une variété torique immersée de façon équivariante (pas nécessairement normale). Fil: Dickenstein, Alicia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: di Rocco, Sandra. Royal Institute Of Technology; Suecia Fil: Piene, Ragni. University Of Oslo; Noruega |
description |
The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-08 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/19058 Dickenstein, Alicia Marcela; di Rocco, Sandra; Piene, Ragni; Higher order duality and toric embeddings; Annales Inst Fourier; Annales de L Institut Fourier; 64; 1; 8-2014; 375-400 0373-0956 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/19058 |
identifier_str_mv |
Dickenstein, Alicia Marcela; di Rocco, Sandra; Piene, Ragni; Higher order duality and toric embeddings; Annales Inst Fourier; Annales de L Institut Fourier; 64; 1; 8-2014; 375-400 0373-0956 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1111.4641 info:eu-repo/semantics/altIdentifier/doi/10.5802/aif.2851 info:eu-repo/semantics/altIdentifier/url/http://aif.cedram.org/item?id=AIF_2014__64_1_375_0 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Annales Inst Fourier |
publisher.none.fl_str_mv |
Annales Inst Fourier |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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