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TitleA flatness property for filtered $scr D$-modules
Author(s) Castro-Jiménez, Francisco J., Granger, Michel
TypeArticle in Journal
AbstractLet $X$ be a complex analytic manifold and ${\\\\scr D}_X$ be the ring of differential operators on $X$. Let ${\\\\scr M}$ be a coherent ${\\\\scr D}_X$-module. Given $x\\\\in X$ and $p$ germs of transverse hypersurfaces, these give rise to $p$ Kashiwara-Malgrange $V$-filtrations and then to a multifiltration on ${\\\\scr M}_x$. C. Sabbah defined and used the notion of adapted fan for this multifiltration. In particular, this fan was used to prove the existence of analytic Bernstein-Sato polynomials.
In the present paper, the authors give a new proof of the existence of an adapted fan. In fact, they prove that the set of closures of the (open) cones of the analytic Gröbner fan as defined in [A. Assi, F. J. Castro-Jiménez and M. Granger, J. Pure Appl. Algebra 164 (2001), no. 1-2, 3--21; MR1854327 (2002k:13046)] is an adapted fan in the sense of Sabbah.
ISSN0034-5318
LanguageEnglish
JournalPubl. Res. Inst. Math. Sci.
Volume43
Number1
Pages121--141
Year2007
Edition0
Translation No
Refereed No
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