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

Synopsis

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.
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};
i4 : B = populateCechComplexCC(I,cc)

o4 = MutableHashTable{...4...}

o4 : MutableHashTable
i5 : scan(keys B, k->print (k=>B#k)) -- CCs of Cech complex BEFORE pruning
{} => {0 => 1}
{0} => {0 => 1, ideal(x ) => 1, ideal(x ) => 1, ideal (x , x ) => 1}
                       2               4                4   2
{0, 1} => {0 => 1, ideal(x ) => 1, ideal(x ) => 1, ideal (x , x ) => 1, ideal(x ) => 1, ideal (x , x ) => 1, ideal (x , x ) => 1, ideal (x , x , x ) => 1}
                          3               4                4   3               2                4   2                3   2                4   3   2
{1} => {0 => 1, ideal(x ) => 1, ideal(x ) => 1, ideal (x , x ) => 1}
                       3               4                4   3

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