Fourier-Laplace transform of a variation of polarized complex Hodge structure, II

Details Fourier-Laplace transform of a variation of polarized complex Hodge structure, II Fourier-Laplace transform of a variation of polarized complex Hodge structure, II

2008-04-28

arxiv.org/abs/0804.4328v3

in New developments in algebraic geometry, integrable systems and mirror symmetry (RIMS, Kyoto, 2008), Adv. Stud. Pure Math.,

Mathematics

Algebraic Geometry

51 pages, revised version, to appear in the proceedings volume of the conference `` New developments in Algebraic Geometry, In

Scientific paper

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.

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