E_1-Formality of Complex Algebraic Varieties
arXiv:1212.3955 · doi:10.2140/agt.2014.14.3049
Abstract
Let X be a smooth complex algebraic variety. Morgan [Mor78] showed that the rational homotopy type of X 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. The result for algebraic morphisms generalizes the Formality Theorem of [DGMS75] for compact Kähler varieties, filling a gap in Morgan's theory concerning functoriality over the rational numbers. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.
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- Model category structures and spectral sequences
- Naturality properties and comparison results for topological and infinitesimal embedded jump loci
- Weight filtration on the cohomology of complex analytic spaces
- Filtered A-infinity structures in complex geometry
- Morgan's mixed Hodge structures and nonabelian Hodge structures