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Hodge theory of the middle convolution. (English) Zbl 1307.14015
Publ. Res. Inst. Math. Sci. 49, No. 4, 761-800 (2013); erratum ibid. 54, No. 2, 427-431 (2018).
For a given irreducible local system on the punctured projective line the Katz algorithm provides a criterion for testing whether this local system is physically rigid. The algorithm (in case of a positive answer) terminates with a rank-one local system. This procedure applies successively tensor product with a rank-one local system and a middle convolution with a Kummer local system. The authors compute the behaviour of Hodge data under tensor product with a unitary rank-one local system and middle convolution with a Kummer unitary rank-one local system for an irreducible variation of a polarized complex Hodge structure on a punctured complex affine line.

MSC:
14D07 Variation of Hodge structures (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
34M99 Ordinary differential equations in the complex domain
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