Abstract
Let be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of is a formal consequence of the differential graded algebra defined by the first term 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.
Citation
Joana Cirici. Francisco Guillén. "$E_1$–formality of complex algebraic varieties." Algebr. Geom. Topol. 14 (5) 3049 - 3079, 2014. https://doi.org/10.2140/agt.2014.14.3049
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