Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence

Serre’s duality theorem implies a symmetry between the Hodge numbers, hp,q = hn−p,n−q, on a compact complex n–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies dimE1p,q=dimE1n−p,n−q\dim E_1^{p,q} = \dim E_1^{n - p,n - q} for all p, q. Adapting an argument...

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Autor principal:	Milivojević Aleksandar
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2020
Materias:	serre symmetry frölicher spectral sequence 32q99 53c56 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c27b854218274db4a920adca1e761217
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spelling	oai:doaj.org-article:c27b854218274db4a920adca1e7612172021-12-02T17:14:47ZAnother proof of the persistence of Serre symmetry in the Frölicher spectral sequence2300-744310.1515/coma-2020-0008https://doaj.org/article/c27b854218274db4a920adca1e7612172020-03-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0008https://doaj.org/toc/2300-7443Serre’s duality theorem implies a symmetry between the Hodge numbers, hp,q = hn−p,n−q, on a compact complex n–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies dimE1p,q=dimE1n−p,n−q\dim E_1^{p,q} = \dim E_1^{n - p,n - q} for all p, q. Adapting an argument of Chern, Hirzebruch, and Serre [3] in an obvious way, in this short note we observe that this “Serre symmetry” dimEkp,q=dimEkn−p,n−q\dim E_k^{p,q} = \dim E_k^{n - p,n - q} holds on all subsequent pages of the spectral sequence as well. The argument shows that an analogous statement holds for the Frölicher spectral sequence of an almost complex structure on a nilpotent real Lie group as considered by Cirici and Wilson in [4].Milivojević AleksandarDe Gruyterarticleserre symmetryfrölicher spectral sequence32q9953c56MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 141-144 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	serre symmetry frölicher spectral sequence 32q99 53c56 Mathematics QA1-939
spellingShingle	serre symmetry frölicher spectral sequence 32q99 53c56 Mathematics QA1-939 Milivojević Aleksandar Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
description	Serre’s duality theorem implies a symmetry between the Hodge numbers, hp,q = hn−p,n−q, on a compact complex n–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies dimE1p,q=dimE1n−p,n−q\dim E_1^{p,q} = \dim E_1^{n - p,n - q} for all p, q. Adapting an argument of Chern, Hirzebruch, and Serre [3] in an obvious way, in this short note we observe that this “Serre symmetry” dimEkp,q=dimEkn−p,n−q\dim E_k^{p,q} = \dim E_k^{n - p,n - q} holds on all subsequent pages of the spectral sequence as well. The argument shows that an analogous statement holds for the Frölicher spectral sequence of an almost complex structure on a nilpotent real Lie group as considered by Cirici and Wilson in [4].
format	article
author	Milivojević Aleksandar
author_facet	Milivojević Aleksandar
author_sort	Milivojević Aleksandar
title	Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
title_short	Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
title_full	Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
title_fullStr	Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
title_full_unstemmed	Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
title_sort	another proof of the persistence of serre symmetry in the frölicher spectral sequence
publisher	De Gruyter
publishDate	2020
url	https://doaj.org/article/c27b854218274db4a920adca1e761217
work_keys_str_mv	AT milivojevicaleksandar anotherproofofthepersistenceofserresymmetryinthefrolicherspectralsequence
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Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence

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