Hodge theory of the middle convolution
Algebraic Geometry
2021-08-09 v4 Number Theory
Abstract
We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line. We give applications of these formulas to local systems with G_2-monodromy.
Cite
@article{arxiv.1209.4185,
title = {Hodge theory of the middle convolution},
author = {Michael Dettweiler and Claude Sabbah},
journal= {arXiv preprint arXiv:1209.4185},
year = {2021}
}
Comments
34 pages. Changes in v2 only consist of appropriate references to previous results of Green-Griffiths-Kerr and to a preprint of Kerr-Pearlstein. Revised version v3, 36 pages. A restricted version of v3, without considerations of irregular singularities, published in Publ. RIMS, Kyoto Univ. V4: correction post publication in the statement of Theorem 3.2.3