Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
Algebraic Geometry
2009-09-14 v1 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0909.2201,
title = {Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results},
author = {James Carlson and Mark Green and Phillip Griffiths},
journal= {arXiv preprint arXiv:0909.2201},
year = {2009}
}