The Fr\"olicher spectral sequence can be arbitrarily non degenerate

Laura Bigalke; Sönke Rollenske

The Fr\"olicher spectral sequence can be arbitrarily non degenerate

Algebraic Geometry 2013-11-22 v3 Differential Geometry

Authors: Laura Bigalke , Sönke Rollenske

Abstract

The Fr\"olicher spectral sequence of a compact complex manifold $X$ measures the difference between Dolbeault cohomology and de Rham cohomology. We construct for $n\geq 2$ 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.

Keywords

cohomology theory cohomology spectral sequences

Cite

@article{arxiv.0709.0481,
  title  = {The Fr\"olicher spectral sequence can be arbitrarily non degenerate},
  author = {Laura Bigalke and Sönke Rollenske},
  journal= {arXiv preprint arXiv:0709.0481},
  year   = {2013}
}

Comments

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

The Fr\"olicher spectral sequence can be arbitrarily non degenerate

Abstract

Keywords

Cite

Comments

Related papers