On the geometric degree of the tangent bundle of a smooth algebraic variety

Autores
Jeronimo, Gabriela Tali; Lanciano, Leonardo; Solernó, Pablo Luis
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety V in terms of the geometric degree of V. We first analyze the case of curves, showing an explicit relation between these degrees. In addition, for parametric curves, we obtain upper bounds that are linear in the degree of the given curve. In the case of varieties of arbitrary dimension, we prove general upper bounds for the degrees of the tangent bundle and the tangential variety of V that are exponential in the dimension or co-dimension of V, and a quadratic upper bound that holds for varieties defined by generic polynomials. Finally, we characterize the smooth irreducible varieties with a tangent bundle of minimal degree.
Fil: Jeronimo, Gabriela Tali. 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. Departamento de Ciencias Exactas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Lanciano, Leonardo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Solernó, Pablo Luis. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
GEOMETRIC DEGREE
TANGENT BUNDLE
AFFINE VARIETY
ALGEBRAIC GEOMETRY
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:11336/265407
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/265407
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the geometric degree of the tangent bundle of a smooth algebraic varietySobre el grado geométrico del fibrado tangente de una variedad algebraica suaveJeronimo, Gabriela TaliLanciano, LeonardoSolernó, Pablo LuisGEOMETRIC DEGREETANGENT BUNDLEAFFINE VARIETYALGEBRAIC GEOMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety V in terms of the geometric degree of V. We first analyze the case of curves, showing an explicit relation between these degrees. In addition, for parametric curves, we obtain upper bounds that are linear in the degree of the given curve. In the case of varieties of arbitrary dimension, we prove general upper bounds for the degrees of the tangent bundle and the tangential variety of V that are exponential in the dimension or co-dimension of V, and a quadratic upper bound that holds for varieties defined by generic polynomials. Finally, we characterize the smooth irreducible varieties with a tangent bundle of minimal degree.Fil: Jeronimo, Gabriela Tali. 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. Departamento de Ciencias Exactas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lanciano, Leonardo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Solernó, Pablo Luis. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaUniversidad de Barcelona2025-04info: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/11336/265407Jeronimo, Gabriela Tali; Lanciano, Leonardo; Solernó, Pablo Luis; On the geometric degree of the tangent bundle of a smooth algebraic variety; Universidad de Barcelona; Collectanea Mathematica; 2025; 4-2025; 1-260010-0757CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s13348-025-00474-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s13348-025-00474-yinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2403.10661info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:45Zoai:ri.conicet.gov.ar:11336/265407instacron: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 09:56:45.643CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the geometric degree of the tangent bundle of a smooth algebraic variety
Sobre el grado geométrico del fibrado tangente de una variedad algebraica suave
title On the geometric degree of the tangent bundle of a smooth algebraic variety
spellingShingle On the geometric degree of the tangent bundle of a smooth algebraic variety
Jeronimo, Gabriela Tali
GEOMETRIC DEGREE
TANGENT BUNDLE
AFFINE VARIETY
ALGEBRAIC GEOMETRY
title_short On the geometric degree of the tangent bundle of a smooth algebraic variety
title_full On the geometric degree of the tangent bundle of a smooth algebraic variety
title_fullStr On the geometric degree of the tangent bundle of a smooth algebraic variety
title_full_unstemmed On the geometric degree of the tangent bundle of a smooth algebraic variety
title_sort On the geometric degree of the tangent bundle of a smooth algebraic variety
dc.creator.none.fl_str_mv Jeronimo, Gabriela Tali
Lanciano, Leonardo
Solernó, Pablo Luis
author Jeronimo, Gabriela Tali
author_facet Jeronimo, Gabriela Tali
Lanciano, Leonardo
Solernó, Pablo Luis
author_role author
author2 Lanciano, Leonardo
Solernó, Pablo Luis
author2_role author
author
dc.subject.none.fl_str_mv GEOMETRIC DEGREE
TANGENT BUNDLE
AFFINE VARIETY
ALGEBRAIC GEOMETRY
topic GEOMETRIC DEGREE
TANGENT BUNDLE
AFFINE VARIETY
ALGEBRAIC GEOMETRY
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 present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety V in terms of the geometric degree of V. We first analyze the case of curves, showing an explicit relation between these degrees. In addition, for parametric curves, we obtain upper bounds that are linear in the degree of the given curve. In the case of varieties of arbitrary dimension, we prove general upper bounds for the degrees of the tangent bundle and the tangential variety of V that are exponential in the dimension or co-dimension of V, and a quadratic upper bound that holds for varieties defined by generic polynomials. Finally, we characterize the smooth irreducible varieties with a tangent bundle of minimal degree.
Fil: Jeronimo, Gabriela Tali. 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. Departamento de Ciencias Exactas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Lanciano, Leonardo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Solernó, Pablo Luis. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety V in terms of the geometric degree of V. We first analyze the case of curves, showing an explicit relation between these degrees. In addition, for parametric curves, we obtain upper bounds that are linear in the degree of the given curve. In the case of varieties of arbitrary dimension, we prove general upper bounds for the degrees of the tangent bundle and the tangential variety of V that are exponential in the dimension or co-dimension of V, and a quadratic upper bound that holds for varieties defined by generic polynomials. Finally, we characterize the smooth irreducible varieties with a tangent bundle of minimal degree.
publishDate 2025
dc.date.none.fl_str_mv 2025-04
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/11336/265407
Jeronimo, Gabriela Tali; Lanciano, Leonardo; Solernó, Pablo Luis; On the geometric degree of the tangent bundle of a smooth algebraic variety; Universidad de Barcelona; Collectanea Mathematica; 2025; 4-2025; 1-26
0010-0757
CONICET Digital
CONICET
url http://hdl.handle.net/11336/265407
identifier_str_mv Jeronimo, Gabriela Tali; Lanciano, Leonardo; Solernó, Pablo Luis; On the geometric degree of the tangent bundle of a smooth algebraic variety; Universidad de Barcelona; Collectanea Mathematica; 2025; 4-2025; 1-26
0010-0757
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://link.springer.com/article/10.1007/s13348-025-00474-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s13348-025-00474-y
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2403.10661
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 Universidad de Barcelona
publisher.none.fl_str_mv Universidad de Barcelona
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 13.13397

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