Minimal resolutions of geometric D-modules
| dc.creator | Arcadias, Rémi | |
| dc.date | 2009-03-24 | |
| dc.date.accessioned | 2026-07-07T12:56:02Z | |
| dc.date.available | 2026-07-07T12:56:02Z | |
| dc.description | In this paper, we study minimal free resolutions for modules over rings of linear differential operators. The resolutions we are interested in are adapted to a given filtration, in particular to the so-called V-filtrations. We are interested in the module D_{x,t}f^s associated with germs of functions f_1,...,f_p, which we call a geometric module, and it is endowed with the V-filtration along t_1=...=t_p=0. The Betti numbers of the minimal resolution associated with this data lead to analytical invariants for the germ of space defined by f_1,...,f_p. For p=1, we show that under some natural conditions on f, the computation of the Betti numbers is reduced to a commutative algebra problem. This includes the case of an isolated quasi homogeneous singularity, for which we give explicitely the Betti numbers. Moreover, for an isolated singularity, we characterize the quasi-homogeneity in terms of the minimal resolution. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/0903.4025 | |
| dc.identifier | http://arxiv.org/abs/0903.4025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224453 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.title | Minimal resolutions of geometric D-modules | |
| dc.type | text |