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dc.contributor.author
Walsh, Miguel Nicolás
dc.date.available
2024-02-14T12:50:02Z
dc.date.issued
2023-04-03
dc.identifier.citation
Walsh, Miguel Nicolás; Concentration estimates for algebraic intersections; Johns Hopkins University Press; American Journal Of Mathematics; 145; 2; 3-4-2023; 435-475
dc.identifier.issn
0002-9327
dc.identifier.uri
http://hdl.handle.net/11336/226788
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Johns Hopkins University Press
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
INCIDENCE GEOMETRY
dc.subject
POLYNOMIAL METHOD
dc.subject
DISCRETE GEOMETRY
dc.subject
INTERSECTION THEORY
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Concentration estimates for algebraic intersections
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-02-02T15:07:38Z
dc.journal.volume
145
dc.journal.number
2
dc.journal.pagination
435-475
dc.journal.pais
Estados Unidos
dc.description.fil
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
dc.journal.title
American Journal Of Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1906.05843
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