| Title:
|
$E_1$-degeneration and $d'd''$-lemma (English) |
| Author:
|
Chen, Tai-Wei |
| Author:
|
Ho, Chung-I |
| Author:
|
Teh, Jyh-Haur |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
155-162 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a double complex $(A, d', d'')$, we show that if it satisfies the $d'd''$-lemma and the spectral sequence $\{E^{p, q}_r\}$ induced by $A$ does not degenerate at $E_0$, then it degenerates at $E_1$. We apply this result to prove the degeneration at $E_1$ of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of $d'd''$-lemma. (English) |
| Keyword:
|
$\partial\overline{\partial}$-lemma |
| Keyword:
|
Hodge-de Rham spectral sequence |
| Keyword:
|
$E_1$-degeneration |
| Keyword:
|
bi-generalized Hermitian manifold |
| MSC:
|
53C05 |
| MSC:
|
55T05 |
| idZBL:
|
Zbl 06604498 |
| idMR:
|
MR3513441 |
| DOI:
|
10.14712/1213-7243.2015.156 |
| . |
| Date available:
|
2016-07-05T15:02:18Z |
| Last updated:
|
2018-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145757 |
| . |
| Reference:
|
[C] Cavalcanti G.: New aspects of the $dd^c$-lemma.Oxford Univ. DPhil. thesis, arXiv:math/0501406v1[math.DG]. |
| Reference:
|
[Ca07] Cavalcanti G.: Introduction to generalized complex geometry.impa, 26-Col´oquio Brasileiro de Matem´atica, 2007. Zbl 1144.53090, MR 2375780 |
| Reference:
|
[CHT] Chen T.W., Ho C.I., Teh J.H.: Aeppli and Bott-Chern cohomology for bigeneralized Hermitian manifolds and $d'd”$-lemma.J. Geom. Phys. 93 (2015), 40–51. MR 3340172, 10.1016/j.geomphys.2015.03.006 |
| Reference:
|
[DGMS] Deligne P., Griffiths P., Morgan J., Sullivan D.: Real homotopy theory of Kähler manifolds.Invent. Math.29 (1975), no. 3, 245–274. Zbl 0355.55016, MR 0382702 |
| Reference:
|
[G1] Gualtieri M.: Generalized complex geometry.Ann. of Math. 174 (2011), 75–123. Zbl 1235.32020, MR 2811595, 10.4007/annals.2011.174.1.3 |
| Reference:
|
[M] McCleary J.: A User's Guide to Spectral Sequences.2nd edition, Cambridge studies in advanced mathematics, 58, Cambridge University Press, Cambridge, 2001. Zbl 0959.55001, MR 1793722 |
| . |
