Using intersection theory

From the introduction: ``The main goal of this work is to present, together with the basic concepts of intersection theory, a number of concrete examples to illustrate several aspects of the calculations and uses of intersection rings, especially in enumerative geometry. `Òur intention is to indicat...

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Autor: Xambó Descamps, Sebastián|||0000-0001-5056-9818
Tipo de recurso: libro
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/400782
Acceso en línea:https://hdl.handle.net/2117/400782
Access Level:acceso abierto
Palabra clave:Geometry, Algebraic
Geometria algèbrica
Varietats (Matemàtica)
Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes
Classificació AMS::14 Algebraic geometry::14M Special varieties
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
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spelling Using intersection theoryXambó Descamps, Sebastián|||0000-0001-5056-9818Geometry, AlgebraicGeometria algèbricaVarietats (Matemàtica)Classificació AMS::14 Algebraic geometry::14C Cycles and subschemesClassificació AMS::14 Algebraic geometry::14M Special varietiesÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraicaFrom the introduction: ``The main goal of this work is to present, together with the basic concepts of intersection theory, a number of concrete examples to illustrate several aspects of the calculations and uses of intersection rings, especially in enumerative geometry. `Òur intention is to indicate the richness of geometrical thinking, in problems whose natural solution is through intersection theory, with a minumum of theoretical build-up. In so doing we hope that it will become increasingly clear that a large harvest is still conceivably to be reaped from the impressively general intersection theory that is currently available. We would also like that these notes be a bridge stretching from contemporary intersection theory to more classical styles of thinking, in particular in enumerative geometry, and also the other way around. Most of the examples were studied by many workers, both classical and modern, and so our job here is, in part, to survey results that are scattered through many sources and involving many generations.'' This monograph collects the material covered by the author in eight lectures given in Mexico in 1992, and it delivers precisely what the introduction promises. Topics include: Intersection rings; Chern classes; Projective bundles; Grassmannians; Flag varieties; Characteristic numbers; Rational equivalence on a blow-up; and Complete quadrics. The results are presented in a cogent fashion, and the examples are chosen very well. Few proofs are provided, and are more often replaced with directions to the established references on the subject. This survey can be recommended to anyone seeking some exposure to classical intersection theory, and to students looking for an engaging introduction to the subject—especially if they take it as a guided tour through the literature. Reviewer: Aluffi, PaoloPeer ReviewedSociedad Matemática Mexicana20242024-01-2720242024-02-01bookhttp://purl.org/coar/resource_type/c_2f33VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookapplication/pdfhttps://hdl.handle.net/2117/400782reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4007822026-05-27T15:37:01Z
dc.title.none.fl_str_mv Using intersection theory
title Using intersection theory
spellingShingle Using intersection theory
Xambó Descamps, Sebastián|||0000-0001-5056-9818
Geometry, Algebraic
Geometria algèbrica
Varietats (Matemàtica)
Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes
Classificació AMS::14 Algebraic geometry::14M Special varieties
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
title_short Using intersection theory
title_full Using intersection theory
title_fullStr Using intersection theory
title_full_unstemmed Using intersection theory
title_sort Using intersection theory
dc.creator.none.fl_str_mv Xambó Descamps, Sebastián|||0000-0001-5056-9818
author Xambó Descamps, Sebastián|||0000-0001-5056-9818
author_facet Xambó Descamps, Sebastián|||0000-0001-5056-9818
author_role author
dc.subject.none.fl_str_mv Geometry, Algebraic
Geometria algèbrica
Varietats (Matemàtica)
Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes
Classificació AMS::14 Algebraic geometry::14M Special varieties
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
topic Geometry, Algebraic
Geometria algèbrica
Varietats (Matemàtica)
Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes
Classificació AMS::14 Algebraic geometry::14M Special varieties
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
description From the introduction: ``The main goal of this work is to present, together with the basic concepts of intersection theory, a number of concrete examples to illustrate several aspects of the calculations and uses of intersection rings, especially in enumerative geometry. `Òur intention is to indicate the richness of geometrical thinking, in problems whose natural solution is through intersection theory, with a minumum of theoretical build-up. In so doing we hope that it will become increasingly clear that a large harvest is still conceivably to be reaped from the impressively general intersection theory that is currently available. We would also like that these notes be a bridge stretching from contemporary intersection theory to more classical styles of thinking, in particular in enumerative geometry, and also the other way around. Most of the examples were studied by many workers, both classical and modern, and so our job here is, in part, to survey results that are scattered through many sources and involving many generations.'' This monograph collects the material covered by the author in eight lectures given in Mexico in 1992, and it delivers precisely what the introduction promises. Topics include: Intersection rings; Chern classes; Projective bundles; Grassmannians; Flag varieties; Characteristic numbers; Rational equivalence on a blow-up; and Complete quadrics. The results are presented in a cogent fashion, and the examples are chosen very well. Few proofs are provided, and are more often replaced with directions to the established references on the subject. This survey can be recommended to anyone seeking some exposure to classical intersection theory, and to students looking for an engaging introduction to the subject—especially if they take it as a guided tour through the literature. Reviewer: Aluffi, Paolo
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-27
2024
2024-02-01
dc.type.none.fl_str_mv book
http://purl.org/coar/resource_type/c_2f33
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/book
format book
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/400782
url https://hdl.handle.net/2117/400782
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Sociedad Matemática Mexicana
publisher.none.fl_str_mv Sociedad Matemática Mexicana
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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