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BMM -- the characteristic cycle of the localized $D$-module

Synopsis

Description

Provided a characteristic cycle in the form {I_1 => m_1, ..., I_k => m_k} with associated prime ideals I1,...,Ik and the multiplicities m1,...,mk of M along them, the routine computes the characteristic cycle of Mf.

The method is based on a geometric formula given by V.Ginsburg in Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327--402. and reinterpreted by J.Briancon, P.Maisonobe and M.Merle in Localisation de systemes differentiels, stratifications de Whitney et condition de Thom, Invent. Math. 117 (1994), 531--550.

A = QQ[x_1,x_2,a_1,a_2]
cc = {ideal A => 1} -- the characteristic ideal of R = CC[x_1,x_2]
cc1 = BMM(cc,x_1) -- cc of R_{x_1}
cc12 = BMM(cc1,x_2) -- cc of R_{x_1x_2}

Caveat

The module has to be a regular holonomic complex-analytic module; while the holomicity can be checked by isHolonomic there is no algorithm to check the regularity.

See also

Ways to use BMM :