Returns an ideal which vanishes on the locus where D is not Cartier.
i1 : R = QQ[x, y, u, v]/ideal(x * y - u * v); |
i2 : D = divisor({1, -3, -5, 8}, {ideal(x, u), ideal(y, v), ideal(x, v), ideal(y, u)}) o2 = -5*Div(x, v) + 8*Div(y, u) + Div(x, u) + -3*Div(y, v) o2 : WeilDivisor on R |
i3 : nonCartierLocus( D ) 5 4 4 4 2 3 3 3 2 3 2 3 3 2 o3 = ideal (v , u*v , y*v , x*v , u v , y*u*v , x*u*v , y v , x v , u v , ------------------------------------------------------------------------ 2 2 2 2 2 2 2 2 3 2 3 2 4 3 3 2 2 y*u v , x*u v , y u*v , x u*v , y v , x v , u v, y*u v, x*u v, y u v, ------------------------------------------------------------------------ 2 2 3 3 4 4 5 4 4 2 3 2 3 3 2 3 2 x u v, y u*v, x u*v, y v, x v, u , y*u , x*u , y u , x u , y u , x u , ------------------------------------------------------------------------ 4 4 5 5 y u, x u, y , x ) o3 : Ideal of R |
If the option IsGraded is set to true (by default it is false), it saturates with respect to the homogeneous maximal ideal.
i4 : R = QQ[x, y, u, v]/ideal(x * y - u * v); |
i5 : D = divisor({1, -3, -5, 8}, {ideal(x, u), ideal(y, v), ideal(x, v), ideal(y, u)}) o5 = -5*Div(x, v) + 8*Div(y, u) + Div(x, u) + -3*Div(y, v) o5 : WeilDivisor on R |
i6 : nonCartierLocus( D, IsGraded => true ) o6 = ideal 1 o6 : Ideal of R |