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# Katz's middle convolution algorithm

Abstract : This is an expository account of Katz's middle convolution operation on local systems over ${\bf P}^1-\{ q_1,\ldots , q_n\}$. We describe the Betti and de Rham versions, and point out that they give isomorphisms between different moduli spaces of local systems, following Völklein, Dettweiler-Reiter, Haraoka-Yokoyama. Kostov's program for applying the Katz algorithm is to say that in the range where middle convolution no longer reduces the rank, one should give a direct construction of local systems. This has been done by Kostov and Crawley-Boevey. We describe here an alternative construction using the notion of cyclotomic harmonic bundles: these are like variations of Hodge structure except that the Hodge decomposition can go around in a circle.
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Preprints, Working Papers, ...
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Cited literature [107 references]

https://hal.archives-ouvertes.fr/hal-00107120
Contributor : Carlos Simpson <>
Submitted on : Wednesday, October 25, 2006 - 9:01:46 AM
Last modification on : Monday, October 12, 2020 - 10:27:24 AM
Long-term archiving on: : Monday, September 20, 2010 - 4:38:42 PM

### Citation

Carlos Simpson. Katz's middle convolution algorithm. 2006. ⟨hal-00107120v2⟩

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