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

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1472-2747

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

646269

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(Dipòsit Digital de la Universitat de Barcelona)

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Title:: $E_{1}$-Formality of complex algebraic varieties
Subject:: 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.
Origin:: Articles publicats en revistes (Matemàtiques i Informàtica)
Idioma:: English
Relationship:: 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
Author/Producer:: Cirici, Joana; Guillén Santos, Francisco
Editor:: Mathematical Sciences Publishers (MSP)
Rights:: (c) Mathematical Sciences Publishers (MSP), 2014; info:eu-repo/semantics/openAccess
Date:: 2015-02-03T11:38:45Z; 2014-11-05
Resource type:: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion
Format:: 31 p.; application/pdf

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3. < dc:creator > Guillén Santos, Francisco </ dc:creator >
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7. < dc:subject > Homotopy theory </ dc:subject >
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19. < dc:language > eng </ dc:language >
20. < dc:relation > Reproducció del document publicat a: http://dx.doi.org/10.2140/agt.2014.14.3049 </ dc:relation >
21. < dc:relation > Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079 </ dc:relation >
22. < dc:relation > http://dx.doi.org/10.2140/agt.2014.14.3049 </ dc:relation >
23. < dc:rights > info:eu-repo/semantics/openAccess </ dc:rights >
24. < dc:rights > (c) Mathematical Sciences Publishers (MSP), 2014 </ dc:rights >
25. < dc:publisher > Mathematical Sciences Publishers (MSP) </ dc:publisher >
26. < dc:source > Articles publicats en revistes (Matemàtiques i Informàtica) </ dc:source >
</ qdc:qualifieddc >

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  1. < dc:title > $E_{1}$-Formality of complex algebraic varieties </ dc:title >
  2. < dc:creator > Cirici, Joana </ dc:creator >
  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 >
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