Deformation Stability of p-SKT and p-HS manifolds

2018/09/01 by Bellitir, Houda · 1 citation
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.00186

Abstract

In this paper, we introduce the notions of p-Hermitian-symplectic and p-pluriclosed compact complex manifolds as generalisations for an arbitrary positive integer p not exceeding the complex dimension of the manifold of the standard notions of Hermitian-symplectic and SKT manifolds that correspond to the case p=1. We then notice that these two properties are equivalent on ∂∂-manifolds and go on to prove that in (smooth) complex analytic families of ∂∂-manifolds, they are deformation open. Concerning closedness results, we prove that the cones A_p, resp. C_p, of Aeppli cohomology classes of strictly weakly positive (p,p)-forms Ω that are p-pluriclosed, resp. p-Hermitian-symplectic, must be equal on the limit fibre if they are equal on the other fibres and if some rather weak ∂∂-type assumptions are made on the other fibres.

Cited by

• Deformations of Non-Kähler Hyperbolicity Notions and Modifications of Degenerate Balanced Manifolds

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