Fourier-Laplace transform of a variation of polarized complex Hodge structure, II
Algebraic Geometry
2011-01-04 v3 Complex Variables
Abstract
We show that the limit, by rescaling, of the `new supersymmetric index' attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of complex Hodge structure and prove a E_1 degeneration property for it.
Cite
@article{arxiv.0804.4328,
title = {Fourier-Laplace transform of a variation of polarized complex Hodge structure, II},
author = {Claude Sabbah},
journal= {arXiv preprint arXiv:0804.4328},
year = {2011}
}
Comments
51 pages, revised version, to appear in the proceedings volume of the conference `` New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry", RIMS, Kyoto, Jan. 7-11, 2008