The polynomial method over varieties

Autores
Walsh, Miguel Nicolás
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.
Fil: Walsh, Miguel Nicolás. 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
Materia
Polynomial method
Real algebraic geometry
Incidence geometry
Milnor-Thom
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:11336/143908
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/143908
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The polynomial method over varietiesWalsh, Miguel NicolásPolynomial methodReal algebraic geometryIncidence geometryMilnor-Thomhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.Fil: Walsh, Miguel Nicolás. 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"; ArgentinaSpringer2020-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143908Walsh, Miguel Nicolás; The polynomial method over varieties; Springer; Inventiones Mathematicae; 222; 2; 11-2020; 469-5120020-9910CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00222-020-00975-6info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-020-00975-6info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1811.07865info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:50Zoai:ri.conicet.gov.ar:11336/143908instacron: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 09:50:51.08CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The polynomial method over varieties
title The polynomial method over varieties
spellingShingle The polynomial method over varieties
Walsh, Miguel Nicolás
Polynomial method
Real algebraic geometry
Incidence geometry
Milnor-Thom
title_short The polynomial method over varieties
title_full The polynomial method over varieties
title_fullStr The polynomial method over varieties
title_full_unstemmed The polynomial method over varieties
title_sort The polynomial method over varieties
dc.creator.none.fl_str_mv Walsh, Miguel Nicolás
author Walsh, Miguel Nicolás
author_facet Walsh, Miguel Nicolás
author_role author
dc.subject.none.fl_str_mv Polynomial method
Real algebraic geometry
Incidence geometry
Milnor-Thom
topic Polynomial method
Real algebraic geometry
Incidence geometry
Milnor-Thom
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 establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.
Fil: Walsh, Miguel Nicolás. 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
description We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.
publishDate 2020
dc.date.none.fl_str_mv 2020-11
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/11336/143908
Walsh, Miguel Nicolás; The polynomial method over varieties; Springer; Inventiones Mathematicae; 222; 2; 11-2020; 469-512
0020-9910
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143908
identifier_str_mv Walsh, Miguel Nicolás; The polynomial method over varieties; Springer; Inventiones Mathematicae; 222; 2; 11-2020; 469-512
0020-9910
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00222-020-00975-6
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-020-00975-6
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1811.07865
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 Springer
publisher.none.fl_str_mv Springer
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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