Revista de la Unión Matemática Argentina
versión On-line ISSN 1669-9637
CONSOLE, Sergio. Dolbeault cohomology and deformations of nilmanifolds. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.1, pp. 51-60. ISSN 1669-9637.
In these notes I review some classes of invariant complex structures on nilmanifolds for which the Dolbeault cohomology can be computed by means of invariant forms, in the spirit of Nomizu's theorem for de Rham cohomology. Moreover, deformations of complex structures are discussed. Small deformations remain in some cases invariant, so that, by Kodaira-Spencer theory, Dolbeault cohomology can be still computed using invariant forms.