On the topology of germs of meromorphic functions and its applications

Let f = P/Q be a meromorphic function germ on (Cn+1, 0), where P,Q: (Cn+1, 0) ! (C, 0) are holomorphic germs. The authors [Funktsional. Anal. i Prilozhen. 32 (1998), no. 2, 26–35, 95; MR1647824 (99j:32040)] introduced a notion of Milnor fibers and monodromy operators of the germ f around zero and in...

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Detalhes bibliográficos
Autores: Melle Hernández, Alejandro, Gusein-Zade, Sabir Medgidovich, Luengo Velasco, Ignacio
Formato: artículo
Fecha de publicación:1999
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/57085
Acesso em linha:https://hdl.handle.net/20.500.14352/57085
Access Level:acceso abierto
Palavra-chave:512.7
Germs of meromorphic functions
Milnor fibre
Atypical values
Geometria algebraica
1201.01 Geometría Algebraica
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spelling On the topology of germs of meromorphic functions and its applicationsMelle Hernández, AlejandroGusein-Zade, Sabir MedgidovichLuengo Velasco, Ignacio512.7Germs of meromorphic functionsMilnor fibreAtypical valuesGeometria algebraica1201.01 Geometría AlgebraicaLet f = P/Q be a meromorphic function germ on (Cn+1, 0), where P,Q: (Cn+1, 0) ! (C, 0) are holomorphic germs. The authors [Funktsional. Anal. i Prilozhen. 32 (1998), no. 2, 26–35, 95; MR1647824 (99j:32040)] introduced a notion of Milnor fibers and monodromy operators of the germ f around zero and infinity and discussed their properties in connection with the problem of computing the zeta-function of the monodromy. The paper under review is devoted to a further investigation of the basic properties of topological invariants of f. In particular, in the case when P has an isolated singularity at the origin the authors prove that the Euler characteristic of the Milnor 0-fiber of f is equal to (−1)n(μ(P, 0)−μ(P +tQ, 0)) for general t 2 C, where μ(P, 0) is the Milnor number of P at zero. They also describe a generalization of a formula from [A. Parusiński and P. Pragacz, J. Algebraic Geom. 4 (1995), no. 2, 337–351; MR1311354 (96i:32039)].Nauka. S.-Peterburg. OtdelUniversidad Complutense de Madrid19991999-01-0119991999-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/57085reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/570852026-06-02T12:44:21Z
dc.title.none.fl_str_mv On the topology of germs of meromorphic functions and its applications
title On the topology of germs of meromorphic functions and its applications
spellingShingle On the topology of germs of meromorphic functions and its applications
Melle Hernández, Alejandro
512.7
Germs of meromorphic functions
Milnor fibre
Atypical values
Geometria algebraica
1201.01 Geometría Algebraica
title_short On the topology of germs of meromorphic functions and its applications
title_full On the topology of germs of meromorphic functions and its applications
title_fullStr On the topology of germs of meromorphic functions and its applications
title_full_unstemmed On the topology of germs of meromorphic functions and its applications
title_sort On the topology of germs of meromorphic functions and its applications
dc.creator.none.fl_str_mv Melle Hernández, Alejandro
Gusein-Zade, Sabir Medgidovich
Luengo Velasco, Ignacio
author Melle Hernández, Alejandro
author_facet Melle Hernández, Alejandro
Gusein-Zade, Sabir Medgidovich
Luengo Velasco, Ignacio
author_role author
author2 Gusein-Zade, Sabir Medgidovich
Luengo Velasco, Ignacio
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.7
Germs of meromorphic functions
Milnor fibre
Atypical values
Geometria algebraica
1201.01 Geometría Algebraica
topic 512.7
Germs of meromorphic functions
Milnor fibre
Atypical values
Geometria algebraica
1201.01 Geometría Algebraica
description Let f = P/Q be a meromorphic function germ on (Cn+1, 0), where P,Q: (Cn+1, 0) ! (C, 0) are holomorphic germs. The authors [Funktsional. Anal. i Prilozhen. 32 (1998), no. 2, 26–35, 95; MR1647824 (99j:32040)] introduced a notion of Milnor fibers and monodromy operators of the germ f around zero and infinity and discussed their properties in connection with the problem of computing the zeta-function of the monodromy. The paper under review is devoted to a further investigation of the basic properties of topological invariants of f. In particular, in the case when P has an isolated singularity at the origin the authors prove that the Euler characteristic of the Milnor 0-fiber of f is equal to (−1)n(μ(P, 0)−μ(P +tQ, 0)) for general t 2 C, where μ(P, 0) is the Milnor number of P at zero. They also describe a generalization of a formula from [A. Parusiński and P. Pragacz, J. Algebraic Geom. 4 (1995), no. 2, 337–351; MR1311354 (96i:32039)].
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-01-01
1999
1999-01-01
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/20.500.14352/57085
url https://hdl.handle.net/20.500.14352/57085
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 Nauka. S.-Peterburg. Otdel
publisher.none.fl_str_mv Nauka. S.-Peterburg. Otdel
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 15,301603

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