an:07227758
Zbl 1441.14040
Dettweiler, Michael; Reiter, Stefan
On the Hodge theory of the additive middle convolution
EN
Publ. Res. Inst. Math. Sci. 56, No. 3, 503-537 (2020).
00451477
2020
j
14D07 32G20 32S40 34M99
middle convolution; Hodge theory
In a previous work of \textit{M. Dettweiler} and \textit{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.
Vladimir P. Kostov (Nice)
Zbl 1307.14015