Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results

This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic c...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2009
Hauptverfasser: Carlson, J., Green, M., Griffiths, P.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2009
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/149133
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results / J. Carlson, M. Green, P. Griffiths // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 21 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Carlson, J.
Green, M.
Griffiths, P.
author_facet Carlson, J.
Green, M.
Griffiths, P.
citation_txt Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results / J. Carlson, M. Green, P. Griffiths // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 21 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic cohomology of a homogeneous Pfaffian system. In the last section we discuss how the integrability conditions of an EDS affect the expected dimension of an integral submanifold. The paper ends with some speculation on EDS and Hodge conjecture for Calabi-Yau manifolds.
first_indexed 2025-12-07T17:03:50Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T17:03:50Z
publishDate 2009
publisher Інститут математики НАН України
record_format dspace
spelling Carlson, J.
Green, M.
Griffiths, P.
2019-02-19T17:35:56Z
2019-02-19T17:35:56Z
2009
Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results / J. Carlson, M. Green, P. Griffiths // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 21 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 14C30; 58A15
https://nasplib.isofts.kiev.ua/handle/123456789/149133
This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic cohomology of a homogeneous Pfaffian system. In the last section we discuss how the integrability conditions of an EDS affect the expected dimension of an integral submanifold. The paper ends with some speculation on EDS and Hodge conjecture for Calabi-Yau manifolds.
This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
Article
published earlier
spellingShingle Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
Carlson, J.
Green, M.
Griffiths, P.
title Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
title_full Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
title_fullStr Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
title_full_unstemmed Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
title_short Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
title_sort variations of hodge structure considered as an exterior differential system: old and new results
url https://nasplib.isofts.kiev.ua/handle/123456789/149133
work_keys_str_mv AT carlsonj variationsofhodgestructureconsideredasanexteriordifferentialsystemoldandnewresults
AT greenm variationsofhodgestructureconsideredasanexteriordifferentialsystemoldandnewresults
AT griffithsp variationsofhodgestructureconsideredasanexteriordifferentialsystemoldandnewresults