$E_{1}$-Formality of complex algebraic varieties
Cirici, Joana
Guillén Santos, Francisco
Singularitats (Matemàtica)
Teoria de l'homotopia
Singularities (Mathematics)
Homotopy theory
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.
2015-02-03T11:38:45Z
2015-02-03T11:38:45Z
2014-11-05
2015-02-03T11:38:45Z
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
1472-2747
http://hdl.handle.net/2445/62303
http://dx.doi.org/10.2140/agt.2014.14.3049
646269
eng
Reproducció del document publicat a: http://dx.doi.org/10.2140/agt.2014.14.3049
Algebraic and Geometric Topology, 2014, vol. 14, p. 3049-3079
(c) Mathematical Sciences Publishers (MSP), 2014
info:eu-repo/semantics/openAccess
31 p.
application/pdf
Mathematical Sciences Publishers (MSP)