While small deformations of compact Kahler manifolds are Kahler too, we prove that the cohomological property to be C-infinity-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 Kahler 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 / D., Angella; Tomassini, Adriano. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - 9:3(2011), pp. 403-428. [10.4310/JSG.2011.v9.n3.a5]

On cohomological decomposition of almost-complex manifolds and deformations

TOMASSINI, Adriano
2011-01-01

Abstract

While small deformations of compact Kahler manifolds are Kahler too, we prove that the cohomological property to be C-infinity-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 Kahler 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 / D., Angella; Tomassini, Adriano. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - 9:3(2011), pp. 403-428. [10.4310/JSG.2011.v9.n3.a5]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2379005
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