Hodge theory of the middle convolution

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.

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

References in corpus (2)

• Boundary Components of Mumford-Tate Domains
• Local Fourier transforms and rigidity for D-modules

Cited by in corpus (16)

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• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Calabi--Yau Operators
• Irregular Hodge filtration of some confluent hypergeometric systems
• Hypergeometric Hodge modules
• Classification of Rigid Irregular $G_2$-Connections
• Middle multiplicative convolution and hypergeometric equations
• Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
• Remarks on rigid irreducible meromorphic connections on the projective line
• Hodge-Arakelov inequalities for family of surfaces fibered by curves
• Tautological systems and free divisors
• On the $\ell$-adic Fourier transform and the determinant of the middle convolution
• Irregular Hodge numbers for rigid $G_2$-connections