On geometric Bott-Chern formality and deformations
Nicoletta Tardini, Adriano Tomassini
TL;DR
This paper explores the concept of geometric formality in Bott-Chern and Aeppli cohomologies on complex manifolds, demonstrating that such formality is not preserved under small complex structure deformations.
Contribution
It introduces a notion of geometric formality in Bott-Chern and Aeppli cohomologies and proves its instability under small deformations using Aeppli-Bott-Chern-Massey products.
Findings
Geometric Aeppli-Bott-Chern formality is not stable under small deformations.
Aeppli-Bott-Chern-Massey triple products are used to detect non-stability.
The study advances understanding of cohomological properties in complex geometry.
Abstract
A notion of geometric formality in the context of Bott-Chern and Aeppli cohomologies on a complex manifold is discussed. In particular, by using Aeppli-Bott-Chern-Massey triple products, it is proved that geometric Aeppli-Bott-Chern formality is not stable under small deformations of the complex structure.
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