On the Bicanonical Morphism of quadruple Galois canonical covers

I In this article we study the bicanonical map ϕ2 of quadruple Galois canonical covers X of surfaces of minimal degree. We show that ϕ2 has diverse behavior and exhibits most of the complexities that are possible for a bicanonical map of surfaces of general type, depending on the type of X. There ar...

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Detalhes bibliográficos
Autores: Gallego Rodrigo, Francisco Javier, Purnaprajna, Bangere P.
Tipo de documento: artigo
Data de publicação:2011
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/41932
Acesso em linha:https://hdl.handle.net/20.500.14352/41932
Access Level:Acceso aberto
Palavra-chave:512.7
Surfaces of general type
Bicanonical map
Quadruple Galois canonical covers
Canonical ring
Surfaces of minimal degree
Geometria algebraica
1201.01 Geometría Algebraica
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oai_identifier_str oai:docta.ucm.es:20.500.14352/41932
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spelling On the Bicanonical Morphism of quadruple Galois canonical coversGallego Rodrigo, Francisco JavierPurnaprajna, Bangere P.512.7Surfaces of general typeBicanonical mapQuadruple Galois canonical coversCanonical ringSurfaces of minimal degreeGeometria algebraica1201.01 Geometría AlgebraicaI In this article we study the bicanonical map ϕ2 of quadruple Galois canonical covers X of surfaces of minimal degree. We show that ϕ2 has diverse behavior and exhibits most of the complexities that are possible for a bicanonical map of surfaces of general type, depending on the type of X. There are cases in which ϕ2 is an embedding, and if it so happens, ϕ2 embeds X as a projectively normal variety, and there are cases in which ϕ2 is not an embedding. If the latter, ϕ2 is finite of degree 1, 2 or 4. We also study the canonical ring of X, proving that it is generated in degree less than or equal to 3 and finding the number of generators in each degree. For generators of degree 2 we find a nice general formula which holds for canonical covers of arbitrary degrees. We show that this formula depends only on the geometric and the arithmetic genus of X.American Mathematical SocietyUniversidad Complutense de Madrid20112011-03-0720112011-03-07journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/41932reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/419322026-06-02T12:44:21Z
dc.title.none.fl_str_mv On the Bicanonical Morphism of quadruple Galois canonical covers
title On the Bicanonical Morphism of quadruple Galois canonical covers
spellingShingle On the Bicanonical Morphism of quadruple Galois canonical covers
Gallego Rodrigo, Francisco Javier
512.7
Surfaces of general type
Bicanonical map
Quadruple Galois canonical covers
Canonical ring
Surfaces of minimal degree
Geometria algebraica
1201.01 Geometría Algebraica
title_short On the Bicanonical Morphism of quadruple Galois canonical covers
title_full On the Bicanonical Morphism of quadruple Galois canonical covers
title_fullStr On the Bicanonical Morphism of quadruple Galois canonical covers
title_full_unstemmed On the Bicanonical Morphism of quadruple Galois canonical covers
title_sort On the Bicanonical Morphism of quadruple Galois canonical covers
dc.creator.none.fl_str_mv Gallego Rodrigo, Francisco Javier
Purnaprajna, Bangere P.
author Gallego Rodrigo, Francisco Javier
author_facet Gallego Rodrigo, Francisco Javier
Purnaprajna, Bangere P.
author_role author
author2 Purnaprajna, Bangere P.
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.7
Surfaces of general type
Bicanonical map
Quadruple Galois canonical covers
Canonical ring
Surfaces of minimal degree
Geometria algebraica
1201.01 Geometría Algebraica
topic 512.7
Surfaces of general type
Bicanonical map
Quadruple Galois canonical covers
Canonical ring
Surfaces of minimal degree
Geometria algebraica
1201.01 Geometría Algebraica
description I In this article we study the bicanonical map ϕ2 of quadruple Galois canonical covers X of surfaces of minimal degree. We show that ϕ2 has diverse behavior and exhibits most of the complexities that are possible for a bicanonical map of surfaces of general type, depending on the type of X. There are cases in which ϕ2 is an embedding, and if it so happens, ϕ2 embeds X as a projectively normal variety, and there are cases in which ϕ2 is not an embedding. If the latter, ϕ2 is finite of degree 1, 2 or 4. We also study the canonical ring of X, proving that it is generated in degree less than or equal to 3 and finding the number of generators in each degree. For generators of degree 2 we find a nice general formula which holds for canonical covers of arbitrary degrees. We show that this formula depends only on the geometric and the arithmetic genus of X.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-03-07
2011
2011-03-07
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/41932
url https://hdl.handle.net/20.500.14352/41932
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,223283

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