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Katz's middle convolution algorithm | | Carlos T. Simpson
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17 Oct 2006 | | Subject: | Algebraic Geometry | | Abstract: | This is an expository account of Katz’s middle convolution operation on local systems over ${f P}^1-{q\_1,..., q\_n}$. We describe the Betti and de Rham versions, and point out that they give isomorphisms between different moduli spaces of local systems, following V"olklein, 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. | | Source: | arXiv, math/0610526 | | Services: | Forum | Review | PDF | Favorites | |
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