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TitleMinimal resolutions of geometric D-modules
Author(s) Rémi Arcadias
TypeArticle in Journal
AbstractIn 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 (see Oaku and Takayama (2001) [18] and Granger and Oaku (2004) [9]). 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 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 the Betti numbers explicitly. Moreover, for an isolated singularity, we characterize the quasi-homogeneity in terms of the minimal resolution.
URL http://www.sciencedirect.com/science/article/pii/S002240490900276X
JournalJournal of Pure and Applied Algebra
Pages1477 - 1496
Translation No
Refereed No