| Katz's middle convolution algorithm (2006) | |||||||||||||
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 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. | |||||||||||||
Publication details | |||||||||||||
| |||||||||||||
Cited publications (24) | |||||||||||||