$E_{1}$-Formality of complex algebraic varieties
Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/62303 |
| Acceso en línea: | https://hdl.handle.net/2445/62303 |
| Access Level: | acceso abierto |
| Palabra clave: | Singularitats (Matemàtica) Teoria de l'homotopia Singularities (Mathematics) Homotopy theory |
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$E_{1}$-Formality of complex algebraic varietiesCirici, JoanaGuillén Santos, FranciscoSingularitats (Matemàtica)Teoria de l'homotopiaSingularities (Mathematics)Homotopy theoryLet $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.Mathematical Sciences Publishers (MSP)2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/62303Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: http://dx.doi.org/10.2140/agt.2014.14.3049Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079http://dx.doi.org/10.2140/agt.2014.14.3049(c) Mathematical Sciences Publishers (MSP), 2014info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/623032026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
$E_{1}$-Formality of complex algebraic varieties |
| title |
$E_{1}$-Formality of complex algebraic varieties |
| spellingShingle |
$E_{1}$-Formality of complex algebraic varieties Cirici, Joana Singularitats (Matemàtica) Teoria de l'homotopia Singularities (Mathematics) Homotopy theory |
| title_short |
$E_{1}$-Formality of complex algebraic varieties |
| title_full |
$E_{1}$-Formality of complex algebraic varieties |
| title_fullStr |
$E_{1}$-Formality of complex algebraic varieties |
| title_full_unstemmed |
$E_{1}$-Formality of complex algebraic varieties |
| title_sort |
$E_{1}$-Formality of complex algebraic varieties |
| dc.creator.none.fl_str_mv |
Cirici, Joana Guillén Santos, Francisco |
| author |
Cirici, Joana |
| author_facet |
Cirici, Joana Guillén Santos, Francisco |
| author_role |
author |
| author2 |
Guillén Santos, Francisco |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Singularitats (Matemàtica) Teoria de l'homotopia Singularities (Mathematics) Homotopy theory |
| topic |
Singularitats (Matemàtica) Teoria de l'homotopia Singularities (Mathematics) Homotopy theory |
| description |
Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory. |
| publishDate |
2014 |
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2014 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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https://hdl.handle.net/2445/62303 |
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https://hdl.handle.net/2445/62303 |
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Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: http://dx.doi.org/10.2140/agt.2014.14.3049 Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079 http://dx.doi.org/10.2140/agt.2014.14.3049 |
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(c) Mathematical Sciences Publishers (MSP), 2014 info:eu-repo/semantics/openAccess |
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(c) Mathematical Sciences Publishers (MSP), 2014 |
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openAccess |
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application/pdf |
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Mathematical Sciences Publishers (MSP) |
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Mathematical Sciences Publishers (MSP) |
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Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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15.300719 |