Starting with a line in Q computed from the procedure fromPointInP3xP3xP3xP3ToLine, the function computes a surface Y in ℙ(22,34) which is a birational model of a numerical Godeaux surface. Note that because of size of the coefficients, the computations over the rational numbers are very time consuming.
i1 : kk=ZZ/101 o1 = kk o1 : QuotientRing |
i2 : H = precomputedModelInP3xP5(kk);
1 1
o2 : Matrix (kk[w , w , w , w , z , z , z , z , z , z ]) <--- (kk[w , w , w , w , z , z , z , z , z , z ])
0 1 2 3 0 1 2 3 4 5 0 1 2 3 0 1 2 3 4 5
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i3 : pt=findPointInP3xP5(kk)
o3 = | 2 44 16 22 45 -34 -48 -47 47 19 |
1 10
o3 : Matrix kk <--- kk
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i4 : pt1=fromPointInP3xP5ToPointInP3xP3xP3xP3(pt)
o4 = | 38 13 32 1 32 -17 -24 1 5 27 -27 1 46 2 -36 1 |
1 16
o4 : Matrix kk <--- kk
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i5 : line =fromPointInP3xP3xP3xP3ToLine(pt1)
o5 = | 48 32 -24 38 -33 -25 -11 -31 19 33 0 1 |
| 10 46 -47 6 23 -44 -6 20 10 -4 1 0 |
2 12
o5 : Matrix kk <--- kk
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i6 : I = fromLineToGodeauxSurface(line);
o6 : Ideal of kk[x , x , y , y , y , y ]
0 1 0 1 2 3
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i7 : S=ring I o7 = S o7 : PolynomialRing |
i8 : J=eliminate(I,{S_0,S_1});
o8 : Ideal of S
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i9 : P3=kk[support J] o9 = P3 o9 : PolynomialRing |
i10 : betti(J'=sub(J,P3))
0 1
o10 = total: 1 1
0: 1 .
1: . .
2: . .
3: . .
4: . .
5: . .
6: . .
7: . .
8: . 1
o10 : BettiTally
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