Year: 2006
Type: preprint
Abstract: This is an expository account of Katz's middle convolution operation on local systems over ${\bf P}^1-\{q\_1,..., q\_n\}$. We describe the Betti and de Rham versions, and point out that they give isomorphisms between different moduli spaces of local systems, following 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.
Source: arXiv (Cornell University)
Author: Simpson, Carlos T.
Institution: Laboratoire Jean-Alexandre Dieudonné
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949876352