Katz's middle convolution algorithm
| dc.creator | Simpson, Carlos T. | |
| dc.date | 2006-10-17 | |
| dc.date | 2006-10-25 | |
| dc.date.accessioned | 2026-07-07T07:29:09Z | |
| dc.date.available | 2026-07-07T07:29:09Z | |
| dc.description | 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. | |
| dc.description | Submitted to Pure and Applied Math Quarterly, Hirzebruch issue. v2 corrects some history and adds references | |
| dc.identifier | https://arxiv.org/abs/math/0610526 | |
| dc.identifier | http://arxiv.org/abs/math/0610526 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117995 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Katz's middle convolution algorithm | |
| dc.type | text |