Skip to Main content Skip to Navigation
Journal articles

Minimal resolutions of geometric D-modules

Abstract : 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.
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00368826
Contributor : Rémi Arcadias <>
Submitted on : Wednesday, March 18, 2009 - 9:38:28 AM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 8:28:57 PM

Files

article-arcadias.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Rémi Arcadias. Minimal resolutions of geometric D-modules. Journal of Pure and Applied Algebra, Elsevier, 2010, 214, pp.1477-1496. ⟨10.1016/j.jpaa.2009.12.001⟩. ⟨hal-00368826⟩

Share

Metrics

Record views

209

Files downloads

102