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On the Hodge theory of the additive middle convolution. (English) Zbl 1441.14040
In a previous work of M. Dettweiler and C. Sabbah [Publ. Res. Inst. Math. Sci. 49, No. 4, 761–800 (2013; Zbl 1307.14015)], the effect of the additive middle convolution MC\(_{\chi}(V)=V\star L_{\chi}\) of a complex polarized Hodge module \(V\) on \(A^1\) with a Kummer module \(L_{\chi}\) on various local and global Hodge data is determined. This leads to an analog of the Katz algorithm for irreducible rigid local systems in the context of Hodge modules.
In this work, the authors extend these results to the case of the middle convolution \(V\star L\) of two irreducible and nonconstant complex polarized Hodge modules on \(A^1\). It turns out that, to a large extent, the general case can be reduced to the middle convolution with Kummer modules as treated by Dettweiler and Sabbah.
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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