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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19058
Acceder
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network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-09-29T09:46:55Zoai: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:34982025-09-29 09:46:55.507CONICET 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/
eu_rights_str_mv 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
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv 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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score 13.069144

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