Concentration estimates for algebraic intersections

Autores
Walsh, Miguel Nicolás
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the method of degree-reduction that enables it to deal efficiently with higher-dimensional problems and also with high-degree varieties. We obtain sharp bounds that are new even in the case of lines in ℝn and show that besides doubly-ruled varieties, only a certain rare family of varieties can be relevant for the study of incidence questions.
Fil: Walsh, Miguel Nicolás. Universidad de Buenos Aires; Argentina. 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
INCIDENCE GEOMETRY
POLYNOMIAL METHOD
DISCRETE GEOMETRY
INTERSECTION THEORY
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:11336/226788
Acceder
id CONICETDig_140f11f8d4bed8adc32ab19efaf8f16e
oai_identifier_str oai:ri.conicet.gov.ar:11336/226788
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Concentration estimates for algebraic intersectionsWalsh, Miguel NicolásINCIDENCE GEOMETRYPOLYNOMIAL METHODDISCRETE GEOMETRYINTERSECTION THEORYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the method of degree-reduction that enables it to deal efficiently with higher-dimensional problems and also with high-degree varieties. We obtain sharp bounds that are new even in the case of lines in ℝn and show that besides doubly-ruled varieties, only a certain rare family of varieties can be relevant for the study of incidence questions.Fil: Walsh, Miguel Nicolás. Universidad de Buenos Aires; Argentina. 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"; ArgentinaJohns Hopkins University Press2023-04-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/226788Walsh, Miguel Nicolás; Concentration estimates for algebraic intersections; Johns Hopkins University Press; American Journal Of Mathematics; 145; 2; 3-4-2023; 435-4750002-9327CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1906.05843info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:00:28Zoai:ri.conicet.gov.ar:11336/226788instacron: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 10:00:28.789CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Concentration estimates for algebraic intersections
title Concentration estimates for algebraic intersections
spellingShingle Concentration estimates for algebraic intersections
Walsh, Miguel Nicolás
INCIDENCE GEOMETRY
POLYNOMIAL METHOD
DISCRETE GEOMETRY
INTERSECTION THEORY
title_short Concentration estimates for algebraic intersections
title_full Concentration estimates for algebraic intersections
title_fullStr Concentration estimates for algebraic intersections
title_full_unstemmed Concentration estimates for algebraic intersections
title_sort Concentration estimates for algebraic intersections
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 INCIDENCE GEOMETRY
POLYNOMIAL METHOD
DISCRETE GEOMETRY
INTERSECTION THEORY
topic INCIDENCE GEOMETRY
POLYNOMIAL METHOD
DISCRETE GEOMETRY
INTERSECTION THEORY
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 an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the method of degree-reduction that enables it to deal efficiently with higher-dimensional problems and also with high-degree varieties. We obtain sharp bounds that are new even in the case of lines in ℝn and show that besides doubly-ruled varieties, only a certain rare family of varieties can be relevant for the study of incidence questions.
Fil: Walsh, Miguel Nicolás. Universidad de Buenos Aires; Argentina. 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 present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the method of degree-reduction that enables it to deal efficiently with higher-dimensional problems and also with high-degree varieties. We obtain sharp bounds that are new even in the case of lines in ℝn and show that besides doubly-ruled varieties, only a certain rare family of varieties can be relevant for the study of incidence questions.
publishDate 2023
dc.date.none.fl_str_mv 2023-04-03
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/11336/226788
Walsh, Miguel Nicolás; Concentration estimates for algebraic intersections; Johns Hopkins University Press; American Journal Of Mathematics; 145; 2; 3-4-2023; 435-475
0002-9327
CONICET Digital
CONICET
url http://hdl.handle.net/11336/226788
identifier_str_mv Walsh, Miguel Nicolás; Concentration estimates for algebraic intersections; Johns Hopkins University Press; American Journal Of Mathematics; 145; 2; 3-4-2023; 435-475
0002-9327
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1906.05843
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 Johns Hopkins University Press
publisher.none.fl_str_mv Johns Hopkins University Press
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_ 1842269639962263552
score 13.13397

Publicaciones similares