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

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

2009-09-11

arxiv.org/abs/0909.2201v1

SIGMA 5 (2009), 087, 40 pages

Mathematics

Algebraic Geometry

Scientific paper

10.3842/SIGMA.2009.087

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.

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