The polynomial method over varieties

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2019, Director: Martín Sombra

Detalles Bibliográficos
Autor: Rovira Cisterna, Sergi
Tipo de recurso: tesis de maestría
Fecha de publicación:2019
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/159040
Acceso en línea:https://hdl.handle.net/2445/159040
Access Level:acceso abierto
Palabra clave:Varietats algebraiques
Geometria algebraica
Treballs de fi de màster
Algebraic varieties
Algebraic geometry
Master's theses
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spelling The polynomial method over varietiesRovira Cisterna, SergiVarietats algebraiquesGeometria algebraicaTreballs de fi de màsterAlgebraic varietiesAlgebraic geometryMaster's thesesTreballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2019, Director: Martín Sombra[en] In 2010, Guth and Katz introduced the polynomial partitioning theorem as a tool in incidence geometry and in additive combinatorics. This allowed the application of results from algebraic geometry (mainly on intersection theory and on the topology of real algebraic varieties) to the solution of long standing problems, including the celebrated Erdős distinct distances problem. Recently, Walsh has extended the polynomial partitioning method to an arbitrary subvariety. This result opens the way to the application of this method to control the point-hypersurface incidences and, more generally, of variety-variety incidences, in spaces of arbitrary dimension. This final project consists in studying Walsh’s paper, to explain its contents and explore its applications to t his kind of incidence problems.Sombra, Martín2019info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/159040Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc-by-sa (c) Sergi Rovira Cisterna, 2019http://creativecommons.org/licenses/by-sa/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1590402026-05-27T06:46:51Z
dc.title.none.fl_str_mv The polynomial method over varieties
title The polynomial method over varieties
spellingShingle The polynomial method over varieties
Rovira Cisterna, Sergi
Varietats algebraiques
Geometria algebraica
Treballs de fi de màster
Algebraic varieties
Algebraic geometry
Master's theses
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 Rovira Cisterna, Sergi
author Rovira Cisterna, Sergi
author_facet Rovira Cisterna, Sergi
author_role author
dc.contributor.none.fl_str_mv Sombra, Martín
dc.subject.none.fl_str_mv Varietats algebraiques
Geometria algebraica
Treballs de fi de màster
Algebraic varieties
Algebraic geometry
Master's theses
topic Varietats algebraiques
Geometria algebraica
Treballs de fi de màster
Algebraic varieties
Algebraic geometry
Master's theses
description Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2019, Director: Martín Sombra
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/159040
url https://hdl.handle.net/2445/159040
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc-by-sa (c) Sergi Rovira Cisterna, 2019
http://creativecommons.org/licenses/by-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-sa (c) Sergi Rovira Cisterna, 2019
http://creativecommons.org/licenses/by-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869412715027496960
score 15.301603

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