Deformations of cohomology classes and spectral sequences
Abstract
We study spectral sequences as an obstruction theory to deforming cohomology classes via the Rees construction. A filtered complex is interpreted as an equivariant family over the affine line, in which higher spectral sequence differentials arise as obstructions to lifting cohomology classes through infinitesimal neighborhoods of the special fibre. This leads to various geometric and module-theoretic degeneration criteria. We give various applications to Ext spectral sequences for complex Lagrangians and the formality results of Melani-Rubió amongst others. For double complexes, we revisit the Khovanov-Qi decomposition on the Rees side and introduce a two-parameter Rees construction over the affine plane. The higher differentials of the two associated spectral sequences correspond to torsion modules supported on the thickened coordinate axes. We obtain degeneration criteria in terms of these modules and an intrinsic characterisation of the ∂∂̅-lemma.
Related
- Cohomology, Extensions and Deformations of restricted Lie triple systems
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- On the Cohomology Classes of Certain Eisenstein-Kronecker Forms
- Big and nef cohomology classes on compact Kähler spaces
BibTeX
@misc{mladenov2026deformations,
title = {{Deformations of cohomology classes and spectral sequences}},
author = {Borislav Mladenov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32593},
eprint = {2610.32593},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32593},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deformations of cohomology classes and spectral sequences
AU - Borislav Mladenov
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32593
UR - https://arxiv.org/abs/2610.32593
AB - We study spectral sequences as an obstruction theory to deforming cohomology classes via the Rees construction. A filtered complex is interpreted as an equivariant family over the affine line, in which higher spectral sequence differentials arise as obstructions to lifting cohomology classes through infinitesimal neighborhoods of the special fibre. This leads to various geometric and module-theoretic degeneration criteria. We give various applications to Ext spectral sequences for complex Lagrangians and the formality results of Melani-Rubió amongst others. For double complexes, we revisit the Khovanov-Qi decomposition on the Rees side and introduce a two-parameter Rees construction over the affine plane. The higher differentials of the two associated spectral sequences correspond to torsion modules supported on the thickened coordinate axes. We obtain degeneration criteria in terms of these modules and an intrinsic characterisation of the ∂∂̅-lemma.
ER -