While small deformations of compact Kähler manifolds are Kähler too, we prove that the cohomological property to be C∞-pure-and-full is not a stable condition under small deformations. This property, which has been recently introduced and studied by Li and Zhang in [24] and Draghici et al. in [13, 14], is weaker than the Kähler one and characterizes the almost-complex structures inducing a decomposition in cohomology. We also study the stability of this property along curves of almost-complex structures constructed starting from the harmonic representatives in special cohomology classes.

On cohomological decomposition of almost-complex manifolds and deformations

Angella, Daniele;Tomassini, Adriano
2011

Abstract

While small deformations of compact Kähler manifolds are Kähler too, we prove that the cohomological property to be C∞-pure-and-full is not a stable condition under small deformations. This property, which has been recently introduced and studied by Li and Zhang in [24] and Draghici et al. in [13, 14], is weaker than the Kähler one and characterizes the almost-complex structures inducing a decomposition in cohomology. We also study the stability of this property along curves of almost-complex structures constructed starting from the harmonic representatives in special cohomology classes.
2011
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/58300
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