2022/06/24 by Ma, Yi
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.12459
Given a ∂∂-manifold X with trivial canonical bundle and carrying a metric ω such that ∂∂ω=0, we introduce the concept of small deformations of X polarised by the Aeppli cohomology class [ω]A of an SKT metric ω. There is a correspondence between the manifolds polarised by [ω]A in the Kuranishi family of X and the Bott-Chern classes that are primitive in a sense that we define. We also investigate the existence of a primitive element in an arbitrary Bott-Chern primitive class and compare the metrics on the base space of the subfamily of manifolds polarised by [ω]A within the Kuranishi family.