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$E_{1}$-Formality of complex algebraic varieties

Identificadores del recurso

1472-2747

http://hdl.handle.net/2445/62303

646269

Procedencia

(Dipòsit Digital de la Universitat de Barcelona)

Ficha

Título:: $E_{1}$-Formality of complex algebraic varieties
Tema:: Singularitats (Matemàtica); Teoria de l'homotopia; Singularities (Mathematics); Homotopy theory
Descripción:: 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.
Fuente:: Articles publicats en revistes (Matemàtiques i Informàtica)
Idioma:: English
Relación:: 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
Autor/Productor:: Cirici, Joana; Guillén Santos, Francisco
Editor:: Mathematical Sciences Publishers (MSP)
Derechos:: (c) Mathematical Sciences Publishers (MSP), 2014; info:eu-repo/semantics/openAccess
Fecha:: 2015-02-03T11:38:45Z; 2014-11-05
Tipo de recurso:: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion
Formato:: 31 p.; application/pdf

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  3. <dc:creator>Guillén Santos, Francisco</dc:creator>
  4. <dc: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.</dc:description>
  5. <dc:date>2015-02-03T11:38:45Z</dc:date>
  6. <dc:date>2015-02-03T11:38:45Z</dc:date>
  7. <dc:date>2014-11-05</dc:date>
  8. <dc:date>2015-02-03T11:38:45Z</dc:date>
  9. <dc:type>info:eu-repo/semantics/article</dc:type>
  10. <dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
  11. <dc:identifier>1472-2747</dc:identifier>
  12. <dc:identifier>http://hdl.handle.net/2445/62303</dc:identifier>
  13. <dc:identifier>646269</dc:identifier>
  14. <dc:language>eng</dc:language>
  15. <dc:relation>Reproducció del document publicat a: http://dx.doi.org/10.2140/agt.2014.14.3049</dc:relation>
  16. <dc:relation>Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079</dc:relation>
  17. <dc:relation>http://dx.doi.org/10.2140/agt.2014.14.3049</dc:relation>
  18. <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  19. <dc:rights>(c) Mathematical Sciences Publishers (MSP), 2014</dc:rights>
  20. <dc:publisher>Mathematical Sciences Publishers (MSP)</dc:publisher>
  21. <dc:source>Articles publicats en revistes (Matemàtiques i Informàtica)</dc:source>
  </ow:Publication>
</rdf:RDF>