E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei Chen; Chung-I Ho; Jyh-Haur Teh

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 2, page 155-162
  • ISSN: 0010-2628

Abstract

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For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } 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.

How to cite

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Chen, Tai-Wei, Ho, Chung-I, and Teh, Jyh-Haur. "$E_1$-degeneration and $d^{\prime }d^{\prime \prime }$-lemma." Commentationes Mathematicae Universitatis Carolinae 57.2 (2016): 155-162. <http://eudml.org/doc/280128>.

@article{Chen2016,
abstract = {For a double complex $(A, d^\{\prime \}, d^\{\prime \prime \})$, we show that if it satisfies the $d^\{\prime \}d^\{\prime \prime \}$-lemma and the spectral sequence $\lbrace E^\{p, q\}_r\rbrace $ 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 $d^\{\prime \}d^\{\prime \prime \}$-lemma.},
author = {Chen, Tai-Wei, Ho, Chung-I, Teh, Jyh-Haur},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\partial \overline\{\partial \}$-lemma; Hodge-de Rham spectral sequence; $E_1$-degeneration; bi-generalized Hermitian manifold},
language = {eng},
number = {2},
pages = {155-162},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$E_1$-degeneration and $d^\{\prime \}d^\{\prime \prime \}$-lemma},
url = {http://eudml.org/doc/280128},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Chen, Tai-Wei
AU - Ho, Chung-I
AU - Teh, Jyh-Haur
TI - $E_1$-degeneration and $d^{\prime }d^{\prime \prime }$-lemma
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 2
SP - 155
EP - 162
AB - For a double complex $(A, d^{\prime }, d^{\prime \prime })$, we show that if it satisfies the $d^{\prime }d^{\prime \prime }$-lemma and the spectral sequence $\lbrace E^{p, q}_r\rbrace $ 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 $d^{\prime }d^{\prime \prime }$-lemma.
LA - eng
KW - $\partial \overline{\partial }$-lemma; Hodge-de Rham spectral sequence; $E_1$-degeneration; bi-generalized Hermitian manifold
UR - http://eudml.org/doc/280128
ER -

References

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  1. Cavalcanti G., New aspects of the d d c -lemma, Oxford Univ. DPhil. thesis, arXiv:math/0501406v1[math.DG]. 
  2. Cavalcanti G., Introduction to generalized complex geometry, impa, 26-Col´oquio Brasileiro de Matem´atica, 2007. Zbl1144.53090MR2375780
  3. Chen T.W., Ho C.I., Teh J.H., 10.1016/j.geomphys.2015.03.006, J. Geom. Phys. 93 (2015), 40–51. MR3340172DOI10.1016/j.geomphys.2015.03.006
  4. Deligne P., Griffiths P., Morgan J., Sullivan D., Real homotopy theory of Kähler manifolds, Invent. Math.29 (1975), no. 3, 245–274. Zbl0355.55016MR0382702
  5. Gualtieri M., 10.4007/annals.2011.174.1.3, Ann. of Math. 174 (2011), 75–123. Zbl1235.32020MR2811595DOI10.4007/annals.2011.174.1.3
  6. McCleary J., A User's Guide to Spectral Sequences, 2nd edition, Cambridge studies in advanced mathematics, 58, Cambridge University Press, Cambridge, 2001. Zbl0959.55001MR1793722

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