Minimal resolutions of geometric D-modules

dc.creatorArcadias, Rémi
dc.date2009-03-24
dc.date.accessioned2026-07-07T12:56:02Z
dc.date.available2026-07-07T12:56:02Z
dc.descriptionIn 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.description31 pages
dc.identifierhttps://arxiv.org/abs/0903.4025
dc.identifierhttp://arxiv.org/abs/0903.4025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224453
dc.subjectAlgebraic Geometry
dc.subjectRings and Algebras
dc.titleMinimal resolutions of geometric D-modules
dc.typetext

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