Finite determination of regular (a,b)-modules
| dc.creator | Barlet, Daniel | |
| dc.date | 2007-04-23 | |
| dc.date | 2007-09-05 | |
| dc.date.accessioned | 2026-07-07T08:27:22Z | |
| dc.date.available | 2026-07-07T08:27:22Z | |
| dc.description | The concept of (a,b)-module comes from the study the Gauss-Manin lattices of an isolated singularity of a germ of an holomorphic function. It is a very simple ''abstract algebraic structure'', but very rich, whose prototype is the formal completion of the Brieskorn-module of an isolated singularity. The aim of this article is to prove a very basic theorem on regular (a,b)-modules showing that a given regular (a,b)-module is completely characterized by some ''finite order jet'' of its structure. Moreover a very simple bound for such a sufficient order is given in term of the rank and of two very simple invariants : the regularity order which count the number of times you need to apply \ $b^{-1}.a \simeq \partial_z.z$ in order to reach a simple pole (a,b)-module. The second invariant is the ''width'' which corresponds, in the simple pole case, to the maximal integral difference between to eigenvalues of $b^{-1}.a$ (the logarithm of the monodromy). In the computation of examples this theorem is quite helpfull because it tells you at which power of $b$ in the expansions you may stop without loosing any information. | |
| dc.identifier | https://arxiv.org/abs/0704.2995 | |
| dc.identifier | http://arxiv.org/abs/0704.2995 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137249 | |
| dc.subject | Complex Variables | |
| dc.subject | 45F15, 34A30, 32S40 | |
| dc.title | Finite determination of regular (a,b)-modules | |
| dc.type | text |