Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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A Complex Geometry Day

Dolbeault-Massey products and formality of the Dolbeault complex

Andrea Cattaneo (Università degli Studi di Parma)

created by daniele on 28 Mar 2015
modified on 05 May 2015

15 may 2015 -- 11:20

Sala Conferenze, Collegio Puteano, Pisa

Abstract.

The study of the properties of the Dolbeault cohomology of a complex variety has recently addressed to the problem of formality. From an abstract point of view, the Dolbeault algebra is an example of differential bigraded algebra, and it is known that for such objects the presence of non-vanishing Massey products is an obstruction to formality. The advantage of working in the abstract setting is that we can use the minimal model of the Dolbeault complex, which is equivalent to the latter from the cohomological point of view, but which make it easier to detect whether there are non-vanishing Massey products.

The aim of the talk is to show a condition on the Dolbeault complex of a complex variety which ensures the presence of a non-vanishing Dolbeault-Massey product in cohomology. As an application, we will use it in the case of nilmanifolds and solvmanifolds of low dimension, in particular to show the stability of the presence of Dolbeault-Massey products under deformations of the complex structure.

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