Deformations of Fuchsian equations and logarithmic connections
| dc.creator | Szabo, Szilard | |
| dc.date | 2007-03-08 | |
| dc.date | 2008-01-16 | |
| dc.date.accessioned | 2026-07-07T08:54:41Z | |
| dc.date.available | 2026-07-07T08:54:41Z | |
| dc.description | We give a geometric proof to the classical fact that the dimension of the deformations of a given generic Fuchsian equation without changing the semi-simple conjugacy class of its local monodromies (``number of accessory parameters'') is equal to half the dimension of the moduli space of deformations of the associated local system. We do this by constructing a weight 1 Hodge structure on the infinitesimal deformations of logarithmic connections, such that deformations as an equation correspond to the $(1,0)$-part. This answers a question of Nicholas Katz, who noticed the dimension doubling mentioned above. We then show that the Hitchin map restricted to deformations of the Fuchsian equation is a one-to-one etale map. Finally, we give a positive answer to a conjecture of Ohtsuki about the maximal number of apparent singularities for a Fuchsian equation with given semisimple monodromy, and define a Lagrangian foliation of the moduli space of connections whose leaves consist of logarithmic connections that can be realised as Fuchsian equations having apparent singularities in a prescribed finite set. | |
| dc.description | 38 pages, content substantially improved, new results and applications added | |
| dc.identifier | https://arxiv.org/abs/math/0703230 | |
| dc.identifier | http://arxiv.org/abs/math/0703230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146024 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 14H60; 34M35; 32G34 | |
| dc.title | Deformations of Fuchsian equations and logarithmic connections | |
| dc.type | text |