On the degeneration of the Frölicher spectral sequence and small deformations

Abstract

We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.

Keywords

• complex geometry
• spectral sequences
• psueudo-differential operators
• 53c56
• 58c40