On the intersection of ACM curves in $\mathbb{P}$

Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in $\mathbb{P}$ never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the max...

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Detalhes bibliográficos
Autores: Hartshorne, Robin, Miró-Roig, Rosa M. (Rosa Maria)
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/102010
Acesso em linha:https://hdl.handle.net/2445/102010
Access Level:acceso abierto
Palavra-chave:Geometria algebraica
Corbes
Algebraic geometry
Curves
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spelling On the intersection of ACM curves in $\mathbb{P}$Hartshorne, RobinMiró-Roig, Rosa M. (Rosa Maria)Geometria algebraicaCorbesAlgebraic geometryCurvesBezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in $\mathbb{P}$ never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in $\mathbb{P}$. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves.Elsevier B.V.2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/102010Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: http://dx.doi.org/10.1016/j.jpaa.2014.10.009Journal of Pure and Applied Algebra, 2015, vol. 219, num. 8, p. 3195-3213http://dx.doi.org/10.1016/j.jpaa.2014.10.009cc-by-nc-nd (c) Elsevier B.V., 2015http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1020102026-05-27T06:46:51Z
dc.title.none.fl_str_mv On the intersection of ACM curves in $\mathbb{P}$
title On the intersection of ACM curves in $\mathbb{P}$
spellingShingle On the intersection of ACM curves in $\mathbb{P}$
Hartshorne, Robin
Geometria algebraica
Corbes
Algebraic geometry
Curves
title_short On the intersection of ACM curves in $\mathbb{P}$
title_full On the intersection of ACM curves in $\mathbb{P}$
title_fullStr On the intersection of ACM curves in $\mathbb{P}$
title_full_unstemmed On the intersection of ACM curves in $\mathbb{P}$
title_sort On the intersection of ACM curves in $\mathbb{P}$
dc.creator.none.fl_str_mv Hartshorne, Robin
Miró-Roig, Rosa M. (Rosa Maria)
author Hartshorne, Robin
author_facet Hartshorne, Robin
Miró-Roig, Rosa M. (Rosa Maria)
author_role author
author2 Miró-Roig, Rosa M. (Rosa Maria)
author2_role author
dc.subject.none.fl_str_mv Geometria algebraica
Corbes
Algebraic geometry
Curves
topic Geometria algebraica
Corbes
Algebraic geometry
Curves
description Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in $\mathbb{P}$ never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in $\mathbb{P}$. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/102010
url https://hdl.handle.net/2445/102010
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.jpaa.2014.10.009
Journal of Pure and Applied Algebra, 2015, vol. 219, num. 8, p. 3195-3213
http://dx.doi.org/10.1016/j.jpaa.2014.10.009
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier B.V., 2015
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier B.V., 2015
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
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
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