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Divisor :: baseLocus

baseLocus -- Computes the locus where a graded module (or O(D) Weil divisor) is not globally generated.

Synopsis

Description

Given a module M with global sections s1, ..., sd, this computes the locus where the is do not generate M. Given a Weil divisor D, this computes the base locus of O(D). For example, consider the rulings on P1 cross P1.
i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v);
i2 : D = divisor( ideal(x,u) )

o2 = 1*Div(u, x) of R

o2 : WDiv
i3 : baseLocus(D)

o3 = ideal 1

o3 : Ideal of R
Or a point on an eliptic curve
i4 : R = QQ[x,y,z]/ideal(y^2*z-x*(x+z)*(x-z));
i5 : D = divisor(ideal(y, x))

o5 = 1*Div(y, x) of R

o5 : WDiv
i6 : baseLocus(D)

o6 = ideal (y, x)

o6 : Ideal of R
i7 : baseLocus(2*D)

o7 = ideal 1

o7 : Ideal of R

Ways to use baseLocus :