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SegreClasses :: intersectionProduct

intersectionProduct -- A class in the Chow ring of the ambient space representing the Fulton-MacPherson intersection product of two schemes inside a variety

Synopsis

Description

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.

R = makeProductRing({3})
(x,y,z,w) = toSequence gens R
Q = ideal(x*y-z*w)
L1 = ideal(x,w)
L2 = ideal(y,w)
intersectionProduct(L1,L2,Q,Verbose=>true)
intersectionProduct(L1,L1,Q)

Ways to use intersectionProduct :