The Frölicher spectral sequence can be arbitrarily non degenerate

Abstract

The Frölicher spectral sequence of a compact complex manifold $X$ measures the difference between Dolbeault cohomology and de Rham cohomology. We construct for $n\ge 2$ nilmanifolds with left-invariant complex structure $X_n$ such that the $n$-th differential $d_n$ does not vanish. This replaces an earlier incorrect example by the second author.

5 pages, Lemma 2 in v2 incorrect. v3: First author added, new example constructed (by the same method). Shorter Erratum will appear in Math. Ann. as well