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

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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.

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Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079

# metadata.dc.rights[].value
(c) Mathematical Sciences Publishers (MSP), 2014

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
$E_{1}$-Formality of complex algebraic varieties