Details:
Title  A flatness property for filtered $scr D$modules  Author(s)  CastroJiménez, Francisco J., Granger, Michel  Type  Article in Journal  Abstract  Let $X$ 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 $p$ KashiwaraMalgrange $V$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 BernsteinSato 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 GrÃƒÂ¶bner fan as defined in [A. Assi, F. J. CastroJimÃƒÂ©nez and M. Granger, J. Pure Appl. Algebra 164 (2001), no. 12, 321; MR1854327 (2002k:13046)] is an adapted fan in the sense of Sabbah.  ISSN  00345318 
Language  English  Journal  Publ. Res. Inst. Math. Sci.  Volume  43  Number  1  Pages  121141  Year  2007  Edition  0  Translation 
No  Refereed 
No 
