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};(S,E)=setupRings(ZZ/101,n); |
i3 : T1 = (dual res trim (ideal vars E)^2)[1]; |
i4 : a=-{2,2};T2=T1**E^{a}[sum a]; |
i6 : W=beilinsonWindow T2,cohomologyTable(W,-2*n,2*n) 15 16 4 o6 = (0 <-- 0 <-- E <-- E <-- E <-- 0, | 0 0 0 0 0 |) | 0 0 0 0 0 | -2 -1 0 1 2 3 | 0 8 15 0 0 | | 0 4 8 0 0 | | 0 0 0 0 0 | o6 : Sequence |
i7 : T=sloppyTateExtension W; |
i8 : cohomologyTable(T,-{3,3},{3,3}) o8 = | 12h 4 20 36 52 68 84 | | 10h 3 16 29 42 55 68 | | 8h 2 12 22 32 42 52 | | 6h 1 8 15 22 29 36 | | 4h 0 4 8 12 16 20 | | 2h h 0 1 2 3 4 | | 0 2h 4h 6h 8h 10h 12h | 7 7 o8 : Matrix (ZZ[h, k]) <--- (ZZ[h, k]) |
i9 : sT1=strand(T,-{1,1},{1}); |
i10 : cohomologyTable(sT1,-{3,3},{3,3}) o10 = | 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 | | 4h 0 4 8 12 16 20 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | 7 7 o10 : Matrix (ZZ[h, k]) <--- (ZZ[h, k]) |
i11 : sT2=strand(T,{1,1},{0}); |
i12 : cohomologyTable(sT2,-{3,3},{3,3}) o12 = | 0 0 0 0 52 0 0 | | 0 0 0 0 42 0 0 | | 0 0 0 0 32 0 0 | | 0 0 0 0 22 0 0 | | 0 0 0 0 12 0 0 | | 0 0 0 0 2 0 0 | | 0 0 0 0 8h 0 0 | 7 7 o12 : Matrix (ZZ[h, k]) <--- (ZZ[h, k]) |
i13 : sT3=removeZeroTrailingTerms strand(T,{1,-1},{0,1}) 12 o13 = 0 <-- E <-- 0 -1 0 1 o13 : ChainComplex |
i14 : cohomologyTable(sT3,-{3,3},{3,3}) o14 = | 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 12 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | 7 7 o14 : Matrix (ZZ[h, k]) <--- (ZZ[h, k]) |