We compute the strand of T as defined in Tate Resolutions on Products of Projective Spaces Theorem 0.4. If T is (part of) the Tate resolution of a sheaf F, then the I-strand of T through c correponds to the Tate resolution RπJ*(F(c)) where J ={0,...,t-1}- I is the complement and πJ: ℙP →∏j ∈J ℙnj denotes the projection.
i1 : n={1,1};
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i2 : (S,E) = productOfProjectiveSpaces n; |
i3 : T1 = (dual res trim (ideal vars E)^2)[1]; |
i4 : a=-{2,2};T2=T1**E^{a}[sum a];
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i6 : W=beilinsonWindow T2,cohomologyMatrix(W,-2*n,2*n)
15 16 4
o6 = (E <-- E <-- E , | 0 0 0 0 0 |)
| 0 0 0 0 0 |
0 1 2 | 0 8 15 0 0 |
| 0 4 8 0 0 |
| 0 0 0 0 0 |
o6 : Sequence
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i7 : T=tateExtension W; |
i8 : low = -{2,2};high = {2,2};
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i10 : cohomologyMatrix(T,low,high)
o10 = | 3 16 29 42 55 |
| 2 12 22 32 42 |
| 1 8 15 22 29 |
| 0 4 8 12 16 |
| h 0 1 2 3 |
5 5
o10 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i11 : sT1=strand(T,{-1,0},{1});
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i12 : cohomologyMatrix(sT1,low,high)
o12 = | 0 0 0 0 0 |
| 0 0 0 0 0 |
| 1 8 15 22 29 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
5 5
o12 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i13 : sT2=strand(T,{-1,0},{0});
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i14 : cohomologyMatrix(sT2,low,high)
o14 = | 0 16 0 0 0 |
| 0 12 0 0 0 |
| 0 8 0 0 0 |
| 0 4 0 0 0 |
| 0 0 0 0 0 |
5 5
o14 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i15 : sT3=strand(T,{-1,0},{0,1});
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i16 : cohomologyMatrix(sT3, low,high)
o16 = | 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 8 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
5 5
o16 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
|