A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect

Autores
Dickenstein, Alicia Marcela; Nill, Benjamin
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that any smooth lattice polytope P with codegree greater or equal than (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is Q-normal (in the terminology of [11]) and answers partially an adjunction-theoretic conjecture by BeltramettiSommese (see [5],[4],[11]). Also, it follows from [24] that smooth lattice polytopes with this property are precisely strict Cayley polytopes, which completes the answer in [11] of a question in [1] for smooth polytopes.
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Nill, Benjamin. University of Georgia; Estados Unidos
Materia
Toric Manifold
Lattice Polytope
Dual Defect
Hypergeometric Equalities
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:11336/15031
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15031
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual DefectDickenstein, Alicia MarcelaNill, BenjaminToric ManifoldLattice PolytopeDual DefectHypergeometric Equalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that any smooth lattice polytope P with codegree greater or equal than (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is Q-normal (in the terminology of [11]) and answers partially an adjunction-theoretic conjecture by BeltramettiSommese (see [5],[4],[11]). Also, it follows from [24] that smooth lattice polytopes with this property are precisely strict Cayley polytopes, which completes the answer in [11] of a question in [1] for smooth polytopes.Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Nill, Benjamin. University of Georgia; Estados UnidosInternational Press Boston2010-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15031Dickenstein, Alicia Marcela; Nill, Benjamin; A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect; International Press Boston; Mathematical Research Letters; 17; 3; 3-2010; 435-4481073-2780enginfo:eu-repo/semantics/altIdentifier/url/http://intlpress.com/site/pub/files/_fulltext/journals/mrl/2010/0017/0003/MRL-2010-0017-0003-a005.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:37:34Zoai:ri.conicet.gov.ar:11336/15031instacron: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 10:37:34.894CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
title A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
spellingShingle A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
Dickenstein, Alicia Marcela
Toric Manifold
Lattice Polytope
Dual Defect
Hypergeometric Equalities
title_short A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
title_full A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
title_fullStr A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
title_full_unstemmed A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
title_sort A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect
dc.creator.none.fl_str_mv Dickenstein, Alicia Marcela
Nill, Benjamin
author Dickenstein, Alicia Marcela
author_facet Dickenstein, Alicia Marcela
Nill, Benjamin
author_role author
author2 Nill, Benjamin
author2_role author
dc.subject.none.fl_str_mv Toric Manifold
Lattice Polytope
Dual Defect
Hypergeometric Equalities
topic Toric Manifold
Lattice Polytope
Dual Defect
Hypergeometric Equalities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that any smooth lattice polytope P with codegree greater or equal than (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is Q-normal (in the terminology of [11]) and answers partially an adjunction-theoretic conjecture by BeltramettiSommese (see [5],[4],[11]). Also, it follows from [24] that smooth lattice polytopes with this property are precisely strict Cayley polytopes, which completes the answer in [11] of a question in [1] for smooth polytopes.
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Nill, Benjamin. University of Georgia; Estados Unidos
description We show that any smooth lattice polytope P with codegree greater or equal than (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is Q-normal (in the terminology of [11]) and answers partially an adjunction-theoretic conjecture by BeltramettiSommese (see [5],[4],[11]). Also, it follows from [24] that smooth lattice polytopes with this property are precisely strict Cayley polytopes, which completes the answer in [11] of a question in [1] for smooth polytopes.
publishDate 2010
dc.date.none.fl_str_mv 2010-03
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/11336/15031
Dickenstein, Alicia Marcela; Nill, Benjamin; A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect; International Press Boston; Mathematical Research Letters; 17; 3; 3-2010; 435-448
1073-2780
url http://hdl.handle.net/11336/15031
identifier_str_mv Dickenstein, Alicia Marcela; Nill, Benjamin; A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect; International Press Boston; Mathematical Research Letters; 17; 3; 3-2010; 435-448
1073-2780
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://intlpress.com/site/pub/files/_fulltext/journals/mrl/2010/0017/0003/MRL-2010-0017-0003-a005.pdf
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
dc.publisher.none.fl_str_mv International Press Boston
publisher.none.fl_str_mv International Press Boston
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
_version_ 1844614396170469376
score 13.070432

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