Deformation Openness and Closedness of Various Classes of Compact Complex Manifolds; Examples

2011/02/08 by Dan Popovici, Popovici, Dan · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1102.1687

openalex publication_date 2011/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (Kähler, balanced or \it strongly Gauduchon) and those satisfying the ∂∂-lemma or the degeneration at E₁ of the Frölicher spectral sequence, as well as the behaviour of these properties under holomorphic deformations. The emphasis will be placed on the notion of \it strongly Gauduchon (sG) manifolds that we introduced recently in the study of deformation limits of projective and Moishezon manifolds. Various examples of sG and non-sG manifolds are exhibited while a range of constructions already known in the literature are reviewed and reinterpreted from this new standpoint.

Citations

• The Self-Duality Equations on a Riemann Surface

Cited by

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

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