Cirici, Joana
Guillén Santos, Francisco
2015-02-03T11:38:45Z
2015-02-03T11:38:45Z
2014-11-05
1472-2747
http://hdl.handle.net/2445/62303
646269
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.
eng
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(c) Mathematical Sciences Publishers (MSP), 2014
$E_{1}$-Formality of complex algebraic varieties
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