We compute the cohomology of two sheaves supported on an elliptic curve.
i1 : X = Proj(QQ[x,y,z])
o1 = X
o1 : ProjectiveVariety
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i2 : I = ideal(y^2*z-x*(x-z)*(x-11*z))
3 2 2 2
o2 = ideal(- x + 12x z + y z - 11x*z )
o2 : Ideal of QQ[x..z]
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i3 : N = (sheaf module I)/(sheaf module I^2)
o3 = subquotient (| -x3+12x2z+y2z-11xz2 |, | x6-24x5z-2x3y2z+166x4z2+24x2y2z2+y4z2-264x3z3-22xy2z3+121x2z4 |)
1
o3 : coherent sheaf on X, subquotient of OO
X
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i4 : G = OO_X^1/I
o4 = cokernel | -x3+12x2z+y2z-11xz2 |
1
o4 : coherent sheaf on X, quotient of OO
X
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i5 : HH^1(G)
1
o5 = QQ
o5 : QQ-module, free
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i6 : HH^1(N)
9
o6 = QQ
o6 : QQ-module, free
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