Some very non-Kähler manifolds: the Frölicher spectral sequence can be arbitrarily non degenerate

Details Some very non-Kähler manifolds: the Frölicher spectral sequence can be arbitrarily non degenerate Some very non-Kähler manifolds: the Frölicher spectral sequence can be arbitrarily non degenerate

2007-09-04

arxiv.org/abs/0709.0481v2

Math. Ann., 341(3), 623--628, 2008

Mathematics

Algebraic Geometry

5 pages, more elementary proof of the theorem, introduction rewritten, references added

Scientific paper

The Fr\"olicher spectral sequence of a compact complex manifold X measures the difference between Dolbeault cohomology and de Rham cohomology and hence degenerates at the E_1 term if X is K\"ahler. We construct for n>1 nilmanifolds with left-invariant complex structure X_n such that the n-th differential in the spectral sequence does not vanish. This answers a question mentioned in the book of Griffith and Harris.

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