The function computes the model of F(Q) in ℙ3 ×ℙ3 ×ℙ3 ×ℙ3 from the four skew-symmetric matrices whose maximal Pfaffians define the complete intersection variety Q. For a general line in F(Q) the restriction of the skew-symmetric matrices have constant syzygies bi. Conversely, given 4×1 matrices b0,..., b3, the ideal I describes the condition that these four vectors come from a line in Q.
i1 : kk = QQ o1 = QQ o1 : Ring |
i2 : I=precomputedModelInP3xP3xP3xP3(kk);
o2 : Ideal of QQ[b , b , b , b , b , b , b , b , b , b , b , b , b , b , b , b ]
0,0 0,1 0,2 0,3 1,0 1,1 1,2 1,3 2,0 2,1 2,2 2,3 3,0 3,1 3,2 3,3
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i3 : isHomogeneous I o3 = true |
i4 : B=QQ[support I] o4 = B o4 : PolynomialRing |
i5 : fI = res sub(I,B) -- 5.27437 seconds elapsed
1 104 294 288 112 15
o5 = B <-- B <-- B <-- B <-- B <-- B <-- 0
0 1 2 3 4 5 6
o5 : ChainComplex
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i6 : betti fI
0 1 2 3 4 5
o6 = total: 1 104 294 288 112 15
0: 1 . . . . .
1: . . . . . .
2: . . . . . .
3: . . . . . .
4: . . . . . .
5: . . . . . .
6: . 16 6 . . .
7: . 84 272 264 96 12
8: . . . . . .
9: . . . . . .
10: . . . . . .
11: . 4 16 24 16 3
o6 : BettiTally
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The computation of the model takes a some time. For that reason we call the precomputed model.