I, an ideal, at which the local cohomology modules HiI(M) are computed.
cc, a list, the characteristic cycle of a regular holonomic module M
Outputs:
a mutable hash table, with entries corresponding to the direct summands of the chains in the Cech complex
Description
For the ideal I=(f1,...,fk) the routine computes the characteristic cycles of the localized modules Mfi1,...,fik and places them in the corresponding places in the Cech complex.
W = QQ[x_1..x_6, a_1..a_6];
I = minors(2, matrix{{x_1, x_2, x_3}, {x_4, x_5, x_6}});
cc = {ideal W => 1};
B = populateCechComplexCC(I,cc)
scan(keys B, k->print (k=>B#k)) -- CCs of Cech complex BEFORE pruning
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
BMM -- the characteristic cycle of the localized $D$-module
pruneCechComplexCC -- reduction of the Cech complex that produces characteristic cycles of local cohomology modules