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 |