Given a graded module M with degree 0 global sections s1, ..., sd, this computes the locus where the si do not generate M. Given a Weil divisor D, this computes the base locus of O(D). For example, consider the rulings on P1 ×P1.
i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v); |
i2 : D = divisor( ideal(x,u) ) o2 = Div(x, u) o2 : WeilDivisor on R |
i3 : baseLocus(D) o3 = ideal 1 o3 : Ideal of R |
Next we consider an example of a point on an elliptic curve.
i4 : R = QQ[x,y,z]/ideal(y^2*z-x*(x+z)*(x-z)); |
i5 : D = divisor(ideal(y, x)) o5 = Div(y, x) o5 : WeilDivisor on R |
i6 : baseLocus(D) o6 = ideal (y, x) o6 : Ideal of R |
i7 : baseLocus(2*D) o7 = ideal 1 o7 : Ideal of R |