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Title: $E_{1}$-Formality of complex algebraic varieties
Author: Cirici, Joana
Guillén Santos, Francisco
Keywords: Singularitats (Matemàtica)
Teoria de l'homotopia
Singularities (Mathematics)
Homotopy theory
Issue Date: 5-Nov-2014
Publisher: Mathematical Sciences Publishers (MSP)
Abstract: 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.
Note: Reproducció del document publicat a:
It is part of: Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079
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ISSN: 1472-2747
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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