populateCechComplexCC(Ideal,List) -- Cech complex skeleton for the computation of the characteristic cycles of local cohomology modules

Synopsis

• Function: populateCechComplexCC
• Usage:
populateCechComplexCC(I,cc)
• Inputs:
• I, an ideal, at which the local cohomology modules H^i_I(M) are computed.
• cc, a list, the characteristic cycle of a regular holonomic module M
• Outputs:
• , with entries corresponding to the direct summands of the chains in the Cech complex

Description

For the ideal I=(f_1,...,f_k) the routine computes the characteristic cycles of the localized modules M_{f_{i_1},...,f_{i_k}} and places them in the corresponding places in the Cech complex.
 i1 : W = QQ[x_1..x_6, a_1..a_6]; i2 : I = minors(2, matrix{{x_1, x_2, x_3}, {x_4, 0, 0}}); o2 : Ideal of W i3 : cc = {ideal W => 1};

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.

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