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SegreClasses :: projectiveDegree

projectiveDegree -- This method computes a single projective degree of a scheme X inside a scheme Y, where X,Y are subschemes of some product of projective spaces

Synopsis

Description

For subschemes X, Y of ℙn1x...xℙnm this command computes a projective degree associated to h of a subscheme X in the subscheme Y as classes in the Chow ring of ℙn1x...xℙnm. The value returned is an integer. This method is faster if only one projective degree is needed.

R = makeProductRing({3,3})
x = gens(R)
D = minors(2,matrix{{x_0..x_3},{x_4..x_7}})
X = ideal(x_0*x_1,x_1*x_2,x_0*x_2)
A = makeChowRing(R)
pd = projectiveDegrees(X,D,A)
h=A_0^2*A_1^2
pdh=projectiveDegree(X,D,h)
(sum pd)_h==pdh

Ways to use projectiveDegree :