This is the first part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. The main result of this part is a constructibility result for the analytic Gröbner fan of a parametric ideal in the ring of analytic differential operators. In this part, the main tool is the notion of reduced generic standard basis.
"Gröbner fan for analytic $D$-modules with parameters." Proc. Japan Acad. Ser. A Math. Sci. 82 (3) 34 - 39, March 2006. https://doi.org/10.3792/pjaa.82.34