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The Frölicher spectral sequence can be arbitrarily non-degenerate

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An Erratum to this article was published on 22 January 2014

Abstract

The Frölicher spectral sequence of a compact complex manifold X measures the difference between Dolbeault cohomology and de Rham cohomology. If X is Kähler then the spectral sequence collapses at the E 1term and no example with d n  ≠  0 for n > 3 has been described in the literature.We construct for n ≥  2 nilmanifolds with left-invariant complex structure X n such that the n-th differential d n does not vanish. This answers a question mentioned in the book of Griffiths and Harris.

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  1. Universität Bayreuth, Bayreuth, Germany

    Sönke Rollenske

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  1. Sönke Rollenske
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Correspondence to Sönke Rollenske.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00208-013-0996-0.

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Rollenske, S. The Frölicher spectral sequence can be arbitrarily non-degenerate. Math. Ann. 341, 623–628 (2008). https://doi.org/10.1007/s00208-007-0206-z

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  • DOI: https://doi.org/10.1007/s00208-007-0206-z

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