For subschemes X,V of a smooth complete intersection subvariety Y of ℙn1x...xℙnm this command computes the Fulton-MacPherson intersection product of X with V in Y as a class in the Chow ring of ℙn1x...xℙnm. Note that this command requires that Y is a smooth complete intersection subvariety, however this is not checked internally.
i1 : R = makeProductRing({3})
o1 = R
o1 : PolynomialRing
|
i2 : (x,y,z,w) = toSequence gens R o2 = (a, b, c, d) o2 : Sequence |
i3 : Q = ideal(x*y-z*w) o3 = ideal(a*b - c*d) o3 : Ideal of R |
i4 : L1 = ideal(x,w) o4 = ideal (a, d) o4 : Ideal of R |
i5 : L2 = ideal(y,w) o5 = ideal (b, d) o5 : Ideal of R |
i6 : intersectionProduct(L1,L2,Q,Verbose=>true)
2 2
[Y]= H H , alpha= 2H + 2H
1 2 1 2
3 3
Projective degrees= {7H H }
1 2
3 3
s(X,Y)= H H
1 2
3
Segre pullback to diagonal = H
1
2
Chern class = 2H + 2H + 1
1 1
3
o6 = H
1
ZZ[H ]
1
o6 : ------
4
H
1
|
i7 : intersectionProduct(L1,L1,Q) o7 = 0 |