On the Bott-Chern cohomology and balanced Hermitian nilmanifolds

Abstract

The Bott-Chern cohomology of 6-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the $\partial \bar{\partial }$-lemma condition and defined in terms of the Bott-Chern cohomology, and show that the vanishing of some of these invariants is not a closed property under holomorphic deformations. In the balanced case, we determine the spaces that parametrize deformations in type IIB supergravity described by Tseng and Yau in terms of the Bott-Chern cohomology group of bidegree (2,2).

arXiv comment18 pages

References in corpus (8)

• Generalized structures of N=1 vacua
• A scan for new N=1 vacua on twisted tori
• Autour de la cohomologie de Bott-Chern
• The cohomologies of the Iwasawa manifold and of its small deformations
• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
• Invariant complex structures on 6-nilmanifolds: classification, Frölicher spectral sequence and special Hermitian metrics
• Generalized Cohomologies and Supersymmetry