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Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
Інший ID:
2000 Mathematics Subject Classification: 14C30; 58A15
Посилання:
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.
Підтримка:
This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”.
Дата:
2009
Переглядів:
548
Завантажень:
238
Анотація:
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.
