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SpectralSequences :: SpectralSequencePageMap _ List

SpectralSequencePageMap _ List -- The p,q th map on of a spectral sequence page

Synopsis

Description

Returns the p,q th map on a (lower index) spectral sequence page. The relationship $D_{p,q} = D^{-p,-q}$ holds.

Consider the filtered complex $K$ below, obtained by multiplying the minimal free resolution of the rational quartic space curve by successive powers of the irrelevant ideal.

i1 : B = QQ[a..d];
i2 : J = ideal vars B;

o2 : Ideal of B
i3 : C = complete res monomialCurveIdeal(B,{1,3,4});
i4 : K = filteredComplex(J,C,4);

We compute a map on the third page of the spectral sequence associated to $K$.

i5 : E = spectralSequence K

o5 = E

o5 : SpectralSequence
i6 : E^3 .dd_{-1,2}

o6 = {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  1  0  0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  1  0  0 0 0 0 0  0  0  0 0 0 0 -1 0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 1  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 0 1  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  1  0 0 0 0 0  0  0  0 0 0 0 0  1  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  1  0 0 0 0 0  0  0  0 0 0 0 0  1 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 1  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 0 1  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 0 0  -1
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     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
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     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     {0} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0 
     ------------------------------------------------------------------------
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     ------------------------------------------------------------------------
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o6 : Matrix

See also