On the degeneration of the Frölicher spectral sequence and small deformations

We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the sec...

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Autor principal:	Maschio Michele
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2020
Materias:	complex geometry spectral sequences psueudo-differential operators 53c56 58c40 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ccc66577f04f466393588f1f937d63ca
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spelling	oai:doaj.org-article:ccc66577f04f466393588f1f937d63ca2021-12-02T16:36:59ZOn the degeneration of the Frölicher spectral sequence and small deformations2300-744310.1515/coma-2020-0003https://doaj.org/article/ccc66577f04f466393588f1f937d63ca2020-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0003https://doaj.org/toc/2300-7443We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.Maschio MicheleDe Gruyterarticlecomplex geometryspectral sequencespsueudo-differential operators53c5658c40MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 62-72 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	complex geometry spectral sequences psueudo-differential operators 53c56 58c40 Mathematics QA1-939
spellingShingle	complex geometry spectral sequences psueudo-differential operators 53c56 58c40 Mathematics QA1-939 Maschio Michele On the degeneration of the Frölicher spectral sequence and small deformations
description	We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.
format	article
author	Maschio Michele
author_facet	Maschio Michele
author_sort	Maschio Michele
title	On the degeneration of the Frölicher spectral sequence and small deformations
title_short	On the degeneration of the Frölicher spectral sequence and small deformations
title_full	On the degeneration of the Frölicher spectral sequence and small deformations
title_fullStr	On the degeneration of the Frölicher spectral sequence and small deformations
title_full_unstemmed	On the degeneration of the Frölicher spectral sequence and small deformations
title_sort	on the degeneration of the frölicher spectral sequence and small deformations
publisher	De Gruyter
publishDate	2020
url	https://doaj.org/article/ccc66577f04f466393588f1f937d63ca
work_keys_str_mv	AT maschiomichele onthedegenerationofthefrolicherspectralsequenceandsmalldeformations
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On the degeneration of the Frölicher spectral sequence and small deformations

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