Hodge polynomials of the moduli spaces of triples of rank (2,2).

Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this pap...

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Detalles Bibliográficos
Autores: Muñoz, Vicente, Ortega, Daniel, Vázquez Gallo, M. Jesús
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/50580
Acceso en línea:https://hdl.handle.net/20.500.14352/50580
Access Level:acceso abierto
Palabra clave:512.7
Moduli space
Complex curve
Stable triple
Hodge polynomial.
Geometria algebraica
1201.01 Geometría Algebraica
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spelling Hodge polynomials of the moduli spaces of triples of rank (2,2).Muñoz, VicenteOrtega, DanielVázquez Gallo, M. Jesús512.7Moduli spaceComplex curveStable tripleHodge polynomial.Geometria algebraica1201.01 Geometría AlgebraicaLet X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this paper, we determine the Hodge polynomials of the moduli spaces of σ-stable triples with rk(E1) = rk(E2) = 2, using the theory of mixed Hodge structures (in the cases that they are smooth and compact). This gives in particular the Poincar´e polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.Oxford University PressUniversidad Complutense de Madrid20092009-01-0120092009-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/50580reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/505802026-06-02T12:44:21Z
dc.title.none.fl_str_mv Hodge polynomials of the moduli spaces of triples of rank (2,2).
title Hodge polynomials of the moduli spaces of triples of rank (2,2).
spellingShingle Hodge polynomials of the moduli spaces of triples of rank (2,2).
Muñoz, Vicente
512.7
Moduli space
Complex curve
Stable triple
Hodge polynomial.
Geometria algebraica
1201.01 Geometría Algebraica
title_short Hodge polynomials of the moduli spaces of triples of rank (2,2).
title_full Hodge polynomials of the moduli spaces of triples of rank (2,2).
title_fullStr Hodge polynomials of the moduli spaces of triples of rank (2,2).
title_full_unstemmed Hodge polynomials of the moduli spaces of triples of rank (2,2).
title_sort Hodge polynomials of the moduli spaces of triples of rank (2,2).
dc.creator.none.fl_str_mv Muñoz, Vicente
Ortega, Daniel
Vázquez Gallo, M. Jesús
author Muñoz, Vicente
author_facet Muñoz, Vicente
Ortega, Daniel
Vázquez Gallo, M. Jesús
author_role author
author2 Ortega, Daniel
Vázquez Gallo, M. Jesús
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.7
Moduli space
Complex curve
Stable triple
Hodge polynomial.
Geometria algebraica
1201.01 Geometría Algebraica
topic 512.7
Moduli space
Complex curve
Stable triple
Hodge polynomial.
Geometria algebraica
1201.01 Geometría Algebraica
description Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this paper, we determine the Hodge polynomials of the moduli spaces of σ-stable triples with rk(E1) = rk(E2) = 2, using the theory of mixed Hodge structures (in the cases that they are smooth and compact). This gives in particular the Poincar´e polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01
2009
2009-01-01
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/20.500.14352/50580
url https://hdl.handle.net/20.500.14352/50580
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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 15.300719

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