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Mathematics > Complex Variables

arXiv:1305.6709 (math)
[Submitted on 29 May 2013 (v1), last revised 12 May 2017 (this version, v3)]

Title:Cohomologies of deformations of solvmanifolds and closedness of some properties

Authors:Daniele Angella, Hisashi Kasuya
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Abstract:We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of some complex solvmanifolds, and we also get explicit examples, showing in particular that either the $\partial\overline{\partial}$-Lemma or the property that the Hodge and Frölicher spectral sequence degenerates at the first level are not closed under deformations.
Subjects: Complex Variables (math.CV); Differential Geometry (math.DG)
MSC classes: 53C30, 57T15, 32G05
Cite as: arXiv:1305.6709 [math.CV]
  (or arXiv:1305.6709v3 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1305.6709
Journal reference: North-Western European Journal of Mathematics 3 (2017), 75--105

Submission history

From: Daniele Angella [view email]
[v1] Wed, 29 May 2013 07:20:21 UTC (19 KB)
[v2] Fri, 2 Jan 2015 15:00:45 UTC (23 KB)
[v3] Fri, 12 May 2017 14:45:40 UTC (20 KB)
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