On the orbits of plane automorphisms and their stabilizers

Rittatore, Alvaro - Pan, Iván

Resumen:

Let 𝕜 be a perfect field with algebraic closure 𝕜. If 𝐻 is a subgroup of plane automorphisms over 𝕜 and 𝑝 ∈ 𝕜 2 is a point, we describe the subgroup consisting of plane automorphisms which stabilize the orbit of 𝑝 under 𝐻, when this orbit has irreducible closure in 𝕜 2. As an application, we treat the case where 𝐻 is cyclic and the closure of the orbit of 𝑝 is an arbitrary (non-necessarily irreducible) curve.


Detalles Bibliográficos
2023
AUTOMORPHISM OF THE AFFINE PLANE
STABILIZAERS OF ORBITS
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/44821
Acceso abierto
Licencia Creative Commons Atribución (CC - By 4.0)
_version_ 1807522809971212288
author Rittatore, Alvaro
author2 Pan, Iván
author2_role author
author_facet Rittatore, Alvaro
Pan, Iván
author_role author
bitstream.checksum.fl_str_mv 6429389a7df7277b72b7924fdc7d47a9
a0ebbeafb9d2ec7cbb19d7137ebc392c
a34a400dd0046b3aef60f72471c4f991
71ed42ef0a0b648670f707320be37b90
5f5195753d8256db4bd12665d98ffcb0
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
bitstream.url.fl_str_mv http://localhost:8080/xmlui/bitstream/20.500.12008/44821/5/license.txt
http://localhost:8080/xmlui/bitstream/20.500.12008/44821/2/license_url
http://localhost:8080/xmlui/bitstream/20.500.12008/44821/3/license_text
http://localhost:8080/xmlui/bitstream/20.500.12008/44821/4/license_rdf
http://localhost:8080/xmlui/bitstream/20.500.12008/44821/1/29-53v.pdf
collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv Rittatore Alvaro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
Pan Iván, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
dc.creator.none.fl_str_mv Rittatore, Alvaro
Pan, Iván
dc.date.accessioned.none.fl_str_mv 2024-07-17T21:11:27Z
dc.date.available.none.fl_str_mv 2024-07-17T21:11:27Z
dc.date.issued.none.fl_str_mv 2023
dc.description.abstract.none.fl_txt_mv Let 𝕜 be a perfect field with algebraic closure 𝕜. If 𝐻 is a subgroup of plane automorphisms over 𝕜 and 𝑝 ∈ 𝕜 2 is a point, we describe the subgroup consisting of plane automorphisms which stabilize the orbit of 𝑝 under 𝐻, when this orbit has irreducible closure in 𝕜 2. As an application, we treat the case where 𝐻 is cyclic and the closure of the orbit of 𝑝 is an arbitrary (non-necessarily irreducible) curve.
dc.description.es.fl_txt_mv La investigación de contó con el apoyo parcial del CSIC (Udelar), ANII y PEDECIBA.
dc.format.extent.es.fl_str_mv 19 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Rittatore, A y Pan, I. "On the orbits of plane automorphisms and their stabilizers". New York Journal of Mathematics. [en línea] 2023: 1373–1392. 19 h.
dc.identifier.issn.none.fl_str_mv 1076-9803
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/44821
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv EMIS
dc.relation.ispartof.es.fl_str_mv New York Journal of Mathematics, 2023: 1373–1392.
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.other.es.fl_str_mv AUTOMORPHISM OF THE AFFINE PLANE
STABILIZAERS OF ORBITS
dc.title.none.fl_str_mv On the orbits of plane automorphisms and their stabilizers
dc.type.es.fl_str_mv Artículo
dc.type.none.fl_str_mv info:eu-repo/semantics/article
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
description La investigación de contó con el apoyo parcial del CSIC (Udelar), ANII y PEDECIBA.
eu_rights_str_mv openAccess
format article
id COLIBRI_2bc79be471474f0b1dfa488024ee9b8d
identifier_str_mv Rittatore, A y Pan, I. "On the orbits of plane automorphisms and their stabilizers". New York Journal of Mathematics. [en línea] 2023: 1373–1392. 19 h.
1076-9803
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en
network_acronym_str COLIBRI
network_name_str COLIBRI
oai_identifier_str oai:colibri.udelar.edu.uy:20.500.12008/44821
publishDate 2023
reponame_str COLIBRI
repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
spelling Rittatore Alvaro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Pan Iván, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2024-07-17T21:11:27Z2024-07-17T21:11:27Z2023Rittatore, A y Pan, I. "On the orbits of plane automorphisms and their stabilizers". New York Journal of Mathematics. [en línea] 2023: 1373–1392. 19 h.1076-9803https://hdl.handle.net/20.500.12008/44821La investigación de contó con el apoyo parcial del CSIC (Udelar), ANII y PEDECIBA.Let 𝕜 be a perfect field with algebraic closure 𝕜. If 𝐻 is a subgroup of plane automorphisms over 𝕜 and 𝑝 ∈ 𝕜 2 is a point, we describe the subgroup consisting of plane automorphisms which stabilize the orbit of 𝑝 under 𝐻, when this orbit has irreducible closure in 𝕜 2. As an application, we treat the case where 𝐻 is cyclic and the closure of the orbit of 𝑝 is an arbitrary (non-necessarily irreducible) curve.Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-16T15:18:26Z No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 29-53v.pdf: 835715 bytes, checksum: 5f5195753d8256db4bd12665d98ffcb0 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-17T18:09:24Z (GMT) No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 29-53v.pdf: 835715 bytes, checksum: 5f5195753d8256db4bd12665d98ffcb0 (MD5)Made available in DSpace by Seroubian Mabel (mabel.seroubian@seciu.edu.uy) on 2024-07-17T21:11:27Z (GMT). No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 29-53v.pdf: 835715 bytes, checksum: 5f5195753d8256db4bd12665d98ffcb0 (MD5) Previous issue date: 202319 h.application/pdfenengEMISNew York Journal of Mathematics, 2023: 1373–1392.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)AUTOMORPHISM OF THE AFFINE PLANESTABILIZAERS OF ORBITSOn the orbits of plane automorphisms and their stabilizersArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaRittatore, AlvaroPan, IvánLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44821/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/44821/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-820496http://localhost:8080/xmlui/bitstream/20.500.12008/44821/3/license_texta34a400dd0046b3aef60f72471c4f991MD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-824251http://localhost:8080/xmlui/bitstream/20.500.12008/44821/4/license_rdf71ed42ef0a0b648670f707320be37b90MD54ORIGINAL29-53v.pdf29-53v.pdfapplication/pdf835715http://localhost:8080/xmlui/bitstream/20.500.12008/44821/1/29-53v.pdf5f5195753d8256db4bd12665d98ffcb0MD5120.500.12008/448212024-07-17 18:11:27.617oai:colibri.udelar.edu.uy:20.500.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Universidadhttps://udelar.edu.uy/https://www.colibri.udelar.edu.uy/oai/requestmabel.seroubian@seciu.edu.uyUruguayopendoar:47712024-07-25T14:29:31.293587COLIBRI - Universidad de la Repúblicafalse
spellingShingle On the orbits of plane automorphisms and their stabilizers
Rittatore, Alvaro
AUTOMORPHISM OF THE AFFINE PLANE
STABILIZAERS OF ORBITS
status_str publishedVersion
title On the orbits of plane automorphisms and their stabilizers
title_full On the orbits of plane automorphisms and their stabilizers
title_fullStr On the orbits of plane automorphisms and their stabilizers
title_full_unstemmed On the orbits of plane automorphisms and their stabilizers
title_short On the orbits of plane automorphisms and their stabilizers
title_sort On the orbits of plane automorphisms and their stabilizers
topic AUTOMORPHISM OF THE AFFINE PLANE
STABILIZAERS OF ORBITS
url https://hdl.handle.net/20.500.12008/44821

Resultados similares